LMFDB - Embedded newform 54.2.e.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			31.1
Root			$0.500000 + 1.96356i$ of defining polynomial
Character	$\chi$	$=$	54.31
Dual form			54.2.e.b.7.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-1.14517 - 1.29945i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.617090 - 3.49969i) q^{5} +(0.631669 + 1.61276i) q^{6} +(-0.244752 + 0.205371i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.377165 + 2.97620i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.14517 - 1.29945i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.617090 - 3.49969i) q^{5} +(0.631669 + 1.61276i) q^{6} +(-0.244752 + 0.205371i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.377165 + 2.97620i) q^{9} +(-1.77684 + 3.07758i) q^{10} +(0.773091 + 4.38442i) q^{11} +(-0.0419788 - 1.73154i) q^{12} +(4.39657 - 1.60022i) q^{13} +(0.300233 - 0.109276i) q^{14} +(-5.25437 + 3.20587i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.567354 + 0.982686i) q^{17} +(1.37234 - 2.66771i) q^{18} +(-0.928896 - 1.60890i) q^{19} +(2.72228 - 2.28426i) q^{20} +(0.547153 + 0.0828588i) q^{21} +(0.773091 - 4.38442i) q^{22} +(0.110473 + 0.0926974i) q^{23} +(-0.552775 + 1.64147i) q^{24} +(-7.16859 - 2.60915i) q^{25} -4.67874 q^{26} +(4.29935 - 2.91815i) q^{27} -0.319501 q^{28} +(4.09634 + 1.49095i) q^{29} +(6.03396 - 1.21543i) q^{30} +(0.514546 + 0.431755i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.81203 - 6.02551i) q^{33} +(0.869237 - 0.729376i) q^{34} +(0.567702 + 0.983289i) q^{35} +(-2.20199 + 2.03746i) q^{36} +(-3.79438 + 6.57207i) q^{37} +(0.322602 + 1.82957i) q^{38} +(-7.11425 - 3.88062i) q^{39} +(-3.33937 + 1.21543i) q^{40} +(-2.04599 + 0.744678i) q^{41} +(-0.485817 - 0.264999i) q^{42} +(-1.23250 - 6.98988i) q^{43} +(-2.22603 + 3.85559i) q^{44} +(10.1830 + 3.15654i) q^{45} +(-0.0721058 - 0.124891i) q^{46} +(-7.91059 + 6.63778i) q^{47} +(1.08086 - 1.35342i) q^{48} +(-1.19781 + 6.79312i) q^{49} +(5.84389 + 4.90360i) q^{50} +(1.92667 - 0.388093i) q^{51} +(4.39657 + 1.60022i) q^{52} +0.805554 q^{53} +(-5.03813 + 1.27170i) q^{54} +15.8212 q^{55} +(0.300233 + 0.109276i) q^{56} +(-1.02694 + 3.04952i) q^{57} +(-3.33937 - 2.80206i) q^{58} +(0.517966 - 2.93753i) q^{59} +(-6.08577 - 0.921605i) q^{60} +(-2.67705 + 2.24631i) q^{61} +(-0.335846 - 0.581702i) q^{62} +(-0.518913 - 0.805889i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.88720 - 16.3741i) q^{65} +(-6.58267 + 4.01631i) q^{66} +(-6.99437 + 2.54574i) q^{67} +(-1.06628 + 0.388093i) q^{68} +(-0.00605383 - 0.249708i) q^{69} +(-0.197161 - 1.11816i) q^{70} +(4.04928 - 7.01356i) q^{71} +(2.76604 - 1.16146i) q^{72} +(-7.30065 - 12.6451i) q^{73} +(5.81333 - 4.87797i) q^{74} +(4.81879 + 12.3032i) q^{75} +(0.322602 - 1.82957i) q^{76} +(-1.08965 - 0.914324i) q^{77} +(5.35796 + 6.07981i) q^{78} +(11.8279 + 4.30501i) q^{79} +3.55368 q^{80} +(-8.71549 - 2.24503i) q^{81} +2.17729 q^{82} +(5.08715 + 1.85157i) q^{83} +(0.365883 + 0.415177i) q^{84} +(3.08899 + 2.59197i) q^{85} +(-1.23250 + 6.98988i) q^{86} +(-2.75360 - 7.03040i) q^{87} +(3.41047 - 2.86173i) q^{88} +(-2.52624 - 4.37558i) q^{89} +(-8.48932 - 6.44898i) q^{90} +(-0.747430 + 1.29459i) q^{91} +(0.0250421 + 0.142021i) q^{92} +(-0.0281968 - 1.16306i) q^{93} +(9.70378 - 3.53189i) q^{94} +(-6.20385 + 2.25802i) q^{95} +(-1.47857 + 0.902126i) q^{96} +(3.24273 + 18.3904i) q^{97} +(3.44896 - 5.97377i) q^{98} +(-13.3405 + 0.647222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−1.14517	−	1.29945i	−0.661165	−	0.750241i
$3$	−1.14517	−	1.29945i	−0.661165	−	0.750241i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.617090	−	3.49969i	0.275971	−	1.56511i	−0.459889	−	0.887977i	$-0.652111\pi$
$5$	0.617090	−	3.49969i	0.275971	−	1.56511i	0.735860	−	0.677134i	$-0.236778\pi$
$6$	0.631669	+	1.61276i	0.257878	+	0.658406i
$7$	−0.244752	+	0.205371i	−0.0925075	+	0.0776230i	−0.687869	−	0.725835i	$-0.741453\pi$
$7$	−0.244752	+	0.205371i	−0.0925075	+	0.0776230i	0.595361	+	0.803458i	$0.297009\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.377165	+	2.97620i	−0.125722	+	0.992066i
$10$	−1.77684	+	3.07758i	−0.561886	+	0.973216i
$11$	0.773091	+	4.38442i	0.233096	+	1.32195i	0.846587	+	0.532250i	$0.178653\pi$
$11$	0.773091	+	4.38442i	0.233096	+	1.32195i	−0.613491	+	0.789702i	$0.710235\pi$
$12$	−0.0419788	−	1.73154i	−0.0121182	−	0.499853i
$13$	4.39657	−	1.60022i	1.21939	−	0.443822i	0.349439	−	0.936959i	$-0.386372\pi$
$13$	4.39657	−	1.60022i	1.21939	−	0.443822i	0.869951	+	0.493137i	$0.164150\pi$
$14$	0.300233	−	0.109276i	0.0802405	−	0.0292052i
$15$	−5.25437	+	3.20587i	−1.35667	+	0.827751i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.567354	+	0.982686i	−0.137604	+	0.238336i	−0.926589	−	0.376075i	$-0.877273\pi$
$17$	−0.567354	+	0.982686i	−0.137604	+	0.238336i	0.788985	+	0.614412i	$0.210607\pi$
$18$	1.37234	−	2.66771i	0.323463	−	0.628786i
$19$	−0.928896	−	1.60890i	−0.213103	−	0.369106i	0.739581	−	0.673068i	$-0.235024\pi$
$19$	−0.928896	−	1.60890i	−0.213103	−	0.369106i	−0.952684	+	0.303962i	$0.901690\pi$
$20$	2.72228	−	2.28426i	0.608720	−	0.510777i
$21$	0.547153	+	0.0828588i	0.119399	+	0.0180813i
$22$	0.773091	−	4.38442i	0.164824	−	0.934761i
$23$	0.110473	+	0.0926974i	0.0230351	+	0.0193288i	0.654233	−	0.756293i	$-0.272992\pi$
$23$	0.110473	+	0.0926974i	0.0230351	+	0.0193288i	−0.631197	+	0.775622i	$0.717436\pi$
$24$	−0.552775	+	1.64147i	−0.112835	+	0.335065i
$25$	−7.16859	−	2.60915i	−1.43372	−	0.521831i
$26$	−4.67874			−0.917576
$27$	4.29935	−	2.91815i	0.827411	−	0.561598i
$28$	−0.319501			−0.0603800
$29$	4.09634	+	1.49095i	0.760672	+	0.276862i	0.693089	−	0.720852i	$-0.256249\pi$
$29$	4.09634	+	1.49095i	0.760672	+	0.276862i	0.0675824	+	0.997714i	$0.478471\pi$
$30$	6.03396	−	1.21543i	1.10165	−	0.221906i
$31$	0.514546	+	0.431755i	0.0924152	+	0.0775455i	0.687825	−	0.725877i	$-0.258566\pi$
$31$	0.514546	+	0.431755i	0.0924152	+	0.0775455i	−0.595410	+	0.803422i	$0.703010\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	4.81203	−	6.02551i	0.837667	−	1.04891i
$34$	0.869237	−	0.729376i	0.149073	−	0.125087i
$35$	0.567702	+	0.983289i	0.0959592	+	0.166206i
$36$	−2.20199	+	2.03746i	−0.366998	+	0.339577i
$37$	−3.79438	+	6.57207i	−0.623793	+	1.08044i	0.364980	+	0.931015i	$0.381076\pi$
$37$	−3.79438	+	6.57207i	−0.623793	+	1.08044i	−0.988773	+	0.149426i	$0.952258\pi$
$38$	0.322602	+	1.82957i	0.0523330	+	0.296795i
$39$	−7.11425	−	3.88062i	−1.13919	−	0.621397i
$40$	−3.33937	+	1.21543i	−0.528000	+	0.192176i
$41$	−2.04599	+	0.744678i	−0.319529	+	0.116299i	−0.496805	−	0.867862i	$-0.665494\pi$
$41$	−2.04599	+	0.744678i	−0.319529	+	0.116299i	0.177276	+	0.984161i	$0.443271\pi$
$42$	−0.485817	−	0.264999i	−0.0749631	−	0.0408903i
$43$	−1.23250	−	6.98988i	−0.187955	−	1.06595i	−0.922099	−	0.386953i	$-0.873528\pi$
$43$	−1.23250	−	6.98988i	−0.187955	−	1.06595i	0.734144	−	0.678994i	$-0.237584\pi$
$44$	−2.22603	+	3.85559i	−0.335586	+	0.581252i
$45$	10.1830	+	3.15654i	1.51800	+	0.470550i
$46$	−0.0721058	−	0.124891i	−0.0106314	−	0.0184142i
$47$	−7.91059	+	6.63778i	−1.15388	+	0.968219i	−0.999803	−	0.0198400i	$-0.993684\pi$
$47$	−7.91059	+	6.63778i	−1.15388	+	0.968219i	−0.154075	+	0.988059i	$0.549240\pi$
$48$	1.08086	−	1.35342i	0.156008	−	0.195350i
$49$	−1.19781	+	6.79312i	−0.171116	+	0.970446i
$50$	5.84389	+	4.90360i	0.826450	+	0.693474i
$51$	1.92667	−	0.388093i	0.269788	−	0.0543439i
$52$	4.39657	+	1.60022i	0.609695	+	0.221911i
$53$	0.805554			0.110651			0.0553257	−	0.998468i	$-0.482380\pi$
$53$	0.805554			0.110651			0.0553257	+	0.998468i	$0.482380\pi$
$54$	−5.03813	+	1.27170i	−0.685603	+	0.173056i
$55$	15.8212			2.13333
$56$	0.300233	+	0.109276i	0.0401203	+	0.0146026i
$57$	−1.02694	+	3.04952i	−0.136022	+	0.403919i
$58$	−3.33937	−	2.80206i	−0.438481	−	0.367929i
$59$	0.517966	−	2.93753i	0.0674334	−	0.382434i	−0.932349	−	0.361560i	$-0.882244\pi$
$59$	0.517966	−	2.93753i	0.0674334	−	0.382434i	0.999782	−	0.0208736i	$-0.00664476\pi$
$60$	−6.08577	−	0.921605i	−0.785670	−	0.118979i
$61$	−2.67705	+	2.24631i	−0.342761	+	0.287611i	−0.797876	−	0.602822i	$-0.794043\pi$
$61$	−2.67705	+	2.24631i	−0.342761	+	0.287611i	0.455114	+	0.890433i	$0.349598\pi$
$62$	−0.335846	−	0.581702i	−0.0426525	−	0.0738763i
$63$	−0.518913	−	0.805889i	−0.0653769	−	0.101532i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.88720	−	16.3741i	−0.358113	−	2.03096i
$66$	−6.58267	+	4.01631i	−0.810271	+	0.494374i
$67$	−6.99437	+	2.54574i	−0.854498	+	0.311012i	−0.731873	−	0.681441i	$-0.761353\pi$
$67$	−6.99437	+	2.54574i	−0.854498	+	0.311012i	−0.122625	+	0.992453i	$0.539131\pi$
$68$	−1.06628	+	0.388093i	−0.129305	+	0.0470632i
$69$	−0.00605383	−	0.249708i	−0.000728795	−	0.0300614i
$70$	−0.197161	−	1.11816i	−0.0235652	−	0.133645i
$71$	4.04928	−	7.01356i	0.480561	−	0.832356i	−0.519190	−	0.854659i	$-0.673766\pi$
$71$	4.04928	−	7.01356i	0.480561	−	0.832356i	0.999751	+	0.0223028i	$0.00709978\pi$
$72$	2.76604	−	1.16146i	0.325981	−	0.136880i
$73$	−7.30065	−	12.6451i	−0.854477	−	1.48000i	−0.877129	−	0.480254i	$-0.840545\pi$
$73$	−7.30065	−	12.6451i	−0.854477	−	1.48000i	0.0226526	−	0.999743i	$-0.492789\pi$
$74$	5.81333	−	4.87797i	0.675786	−	0.567052i
$75$	4.81879	+	12.3032i	0.556426	+	1.42065i
$76$	0.322602	−	1.82957i	0.0370050	−	0.209866i
$77$	−1.08965	−	0.914324i	−0.124177	−	0.104197i
$78$	5.35796	+	6.07981i	0.606669	+	0.688403i
$79$	11.8279	+	4.30501i	1.33074	+	0.484351i	0.906886	−	0.421377i	$-0.138453\pi$
$79$	11.8279	+	4.30501i	1.33074	+	0.484351i	0.423859	+	0.905728i	$0.360675\pi$
$80$	3.55368			0.397314
$81$	−8.71549	−	2.24503i	−0.968388	−	0.249448i
$82$	2.17729			0.240442
$83$	5.08715	+	1.85157i	0.558387	+	0.203236i	0.605769	−	0.795641i	$-0.292866\pi$
$83$	5.08715	+	1.85157i	0.558387	+	0.203236i	−0.0473820	+	0.998877i	$0.515088\pi$
$84$	0.365883	+	0.415177i	0.0399211	+	0.0452995i
$85$	3.08899	+	2.59197i	0.335048	+	0.281139i
$86$	−1.23250	+	6.98988i	−0.132904	+	0.753738i
$87$	−2.75360	−	7.03040i	−0.295216	−	0.753738i
$88$	3.41047	−	2.86173i	0.363558	−	0.305061i
$89$	−2.52624	−	4.37558i	−0.267781	−	0.463810i	0.700508	−	0.713645i	$-0.252957\pi$
$89$	−2.52624	−	4.37558i	−0.267781	−	0.463810i	−0.968288	+	0.249835i	$0.919624\pi$
$90$	−8.48932	−	6.44898i	−0.894853	−	0.679782i
$91$	−0.747430	+	1.29459i	−0.0783520	+	0.135710i
$92$	0.0250421	+	0.142021i	0.00261082	+	0.0148067i
$93$	−0.0281968	−	1.16306i	−0.00292387	−	0.120604i
$94$	9.70378	−	3.53189i	1.00087	−	0.364286i
$95$	−6.20385	+	2.25802i	−0.636502	+	0.231668i
$96$	−1.47857	+	0.902126i	−0.150906	+	0.0920728i
$97$	3.24273	+	18.3904i	0.329249	+	1.86726i	0.477957	+	0.878383i	$0.341377\pi$
$97$	3.24273	+	18.3904i	0.329249	+	1.86726i	−0.148708	+	0.988881i	$0.547511\pi$
$98$	3.44896	−	5.97377i	0.348398	−	0.603442i
$99$	−13.3405	+	0.647222i	−1.34077	+	0.0650483i
$100$	−3.81433	−	6.60661i	−0.381433	−	0.660661i
$101$	−1.85357	+	1.55533i	−0.184438	+	0.154761i	−0.730332	−	0.683093i	$-0.760634\pi$
$101$	−1.85357	+	1.55533i	−0.184438	+	0.154761i	0.545894	+	0.837854i	$0.316190\pi$
$102$	−1.94322	−	0.294273i	−0.192407	−	0.0291374i
$103$	0.346489	−	1.96504i	0.0341406	−	0.193621i	−0.962967	−	0.269618i	$-0.913103\pi$
$103$	0.346489	−	1.96504i	0.0341406	−	0.193621i	0.997108	+	0.0759967i	$0.0242138\pi$
$104$	−3.58412	−	3.00743i	−0.351452	−	0.294903i
$105$	0.627623	−	1.86374i	0.0612498	−	0.181882i
$106$	−0.756973	−	0.275516i	−0.0735238	−	0.0267605i
$107$	8.87072			0.857565			0.428783	−	0.903408i	$-0.358943\pi$
$107$	8.87072			0.857565			0.428783	+	0.903408i	$0.358943\pi$
$108$	5.16924	+	0.528140i	0.497411	+	0.0508203i
$109$	−1.97204			−0.188887			−0.0944434	−	0.995530i	$-0.530107\pi$
$109$	−1.97204			−0.188887			−0.0944434	+	0.995530i	$0.530107\pi$
$110$	−14.8671	−	5.41116i	−1.41752	−	0.515934i
$111$	12.8853	−	2.59551i	1.22302	−	0.246355i
$112$	−0.244752	−	0.205371i	−0.0231269	−	0.0194058i
$113$	−1.67200	+	9.48237i	−0.157288	+	0.892026i	0.799375	+	0.600832i	$0.205164\pi$
$113$	−1.67200	+	9.48237i	−0.157288	+	0.892026i	−0.956664	+	0.291195i	$0.905947\pi$
$114$	2.00801	−	2.51438i	0.188067	−	0.235493i
$115$	0.392584	−	0.329417i	0.0366087	−	0.0307183i
$116$	2.17962	+	3.77521i	0.202372	+	0.350519i
$117$	3.10434	+	13.6886i	0.286996	+	1.26551i
$118$	−1.49142	+	2.58322i	−0.137297	+	0.237805i
$119$	−0.0629545	−	0.357033i	−0.00577103	−	0.0327291i
$120$	5.40355	+	2.94748i	0.493274	+	0.269067i
$121$	−8.28884	+	3.01689i	−0.753530	+	0.274263i
$122$	3.28389	−	1.19524i	0.297309	−	0.108212i
$123$	3.31068	+	1.80588i	0.298514	+	0.162831i
$124$	0.116638	+	0.661487i	0.0104744	+	0.0594033i
$125$	−4.67070	+	8.08988i	−0.417760	+	0.723581i
$126$	0.211989	+	0.934766i	0.0188855	+	0.0832756i
$127$	−0.0796049	−	0.137880i	−0.00706379	−	0.0122348i	0.862472	−	0.506105i	$-0.168915\pi$
$127$	−0.0796049	−	0.137880i	−0.00706379	−	0.0122348i	−0.869536	+	0.493870i	$0.835582\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−7.67160	+	9.60619i	−0.675447	+	0.845778i
$130$	−2.88720	+	16.3741i	−0.253224	+	1.43611i
$131$	−7.26657	−	6.09738i	−0.634883	−	0.532730i	0.267559	−	0.963542i	$-0.413783\pi$
$131$	−7.26657	−	6.09738i	−0.634883	−	0.532730i	−0.902442	+	0.430811i	$0.858227\pi$
$132$	7.55935	−	1.52269i	0.657957	−	0.132533i
$133$	0.557770	+	0.203012i	0.0483648	+	0.0176033i
$134$	7.44325			0.642999
$135$	−7.55953	−	16.8472i	−0.650621	−	1.44997i
$136$	1.13471			0.0973004
$137$	−11.0032	−	4.00484i	−0.940067	−	0.342156i	−0.173875	−	0.984768i	$-0.555629\pi$
$137$	−11.0032	−	4.00484i	−0.940067	−	0.342156i	−0.766192	+	0.642611i	$0.777851\pi$
$138$	−0.0797166	+	0.236720i	−0.00678593	+	0.0201509i
$139$	−4.02194	−	3.37481i	−0.341136	−	0.286247i	0.456083	−	0.889937i	$-0.349252\pi$
$139$	−4.02194	−	3.37481i	−0.341136	−	0.286247i	−0.797219	+	0.603690i	$0.793696\pi$
$140$	−0.197161	+	1.11816i	−0.0166631	+	0.0945014i
$141$	17.6845	+	2.67807i	1.48930	+	0.225534i
$142$	−6.20385	+	5.20565i	−0.520616	+	0.436849i
$143$	10.4150	+	18.0393i	0.870946	+	1.50852i
$144$	−2.99648	+	0.145376i	−0.249706	+	0.0121147i
$145$	7.74567	−	13.4159i	0.643243	−	1.11413i
$146$	2.53549	+	14.3795i	0.209839	+	1.19005i
$147$	10.1991	−	6.22279i	0.841204	−	0.513247i
$148$	−7.13111	+	2.59551i	−0.586174	+	0.213350i
$149$	15.3097	−	5.57227i	1.25422	−	0.456499i	0.372394	−	0.928075i	$-0.378537\pi$
$149$	15.3097	−	5.57227i	1.25422	−	0.456499i	0.881825	+	0.471576i	$0.156315\pi$
$150$	−0.320242	−	13.2093i	−0.0261476	−	1.07854i
$151$	−2.71203	−	15.3807i	−0.220702	−	1.25166i	−0.870734	−	0.491754i	$-0.836356\pi$
$151$	−2.71203	−	15.3807i	−0.220702	−	1.25166i	0.650033	−	0.759906i	$-0.274755\pi$
$152$	−0.928896	+	1.60890i	−0.0753434	+	0.130499i
$153$	−2.71068	−	2.05919i	−0.219146	−	0.166476i
$154$	0.711218	+	1.23187i	0.0573116	+	0.0992665i
$155$	1.82853	−	1.53432i	0.146871	−	0.123240i
$156$	−2.95541	−	7.54568i	−0.236623	−	0.604138i
$157$	3.06168	−	17.3637i	0.244349	−	1.38577i	−0.577651	−	0.816284i	$-0.696030\pi$
$157$	3.06168	−	17.3637i	0.244349	−	1.38577i	0.822000	−	0.569488i	$-0.192859\pi$
$158$	−9.64221	−	8.09077i	−0.767093	−	0.643667i
$159$	−0.922498	−	1.04678i	−0.0731588	−	0.0830151i
$160$	−3.33937	−	1.21543i	−0.264000	−	0.0960882i
$161$	−0.0460757			−0.00363128
$162$	7.42204	+	5.09052i	0.583130	+	0.399949i
$163$	−15.8801			−1.24382			−0.621912	−	0.783087i	$-0.713644\pi$
$163$	−15.8801			−1.24382			−0.621912	+	0.783087i	$0.713644\pi$
$164$	−2.04599	−	0.744678i	−0.159765	−	0.0581496i
$165$	−18.1180	−	20.5589i	−1.41048	−	1.60051i
$166$	−4.14708	−	3.47981i	−0.321876	−	0.270086i
$167$	−2.35787	+	13.3721i	−0.182457	+	1.03477i	0.746722	+	0.665137i	$0.231627\pi$
$167$	−2.35787	+	13.3721i	−0.182457	+	1.03477i	−0.929179	+	0.369630i	$0.879484\pi$
$168$	−0.201819	−	0.515278i	−0.0155707	−	0.0397546i
$169$	6.81058	−	5.71475i	0.523891	−	0.439596i
$170$	−2.01620	−	3.49215i	−0.154635	−	0.267836i
$171$	5.13874	−	2.15776i	0.392969	−	0.165008i
$172$	3.54885	−	6.14680i	0.270598	−	0.468689i
$173$	1.11906	+	6.34650i	0.0850805	+	0.482516i	0.997339	+	0.0729010i	$0.0232257\pi$
$173$	1.11906	+	6.34650i	0.0850805	+	0.482516i	−0.912259	+	0.409615i	$0.865663\pi$
$174$	0.182995	+	7.54820i	0.0138728	+	0.572228i
$175$	2.29037	−	0.833627i	0.173136	−	0.0630163i
$176$	−4.18356	+	1.52269i	−0.315348	+	0.114777i
$177$	−4.41035	+	2.69090i	−0.331502	+	0.202261i
$178$	0.877354	+	4.97572i	0.0657605	+	0.372946i
$179$	6.25613	−	10.8359i	0.467605	−	0.809915i	−0.531710	−	0.846927i	$-0.678450\pi$
$179$	6.25613	−	10.8359i	0.467605	−	0.809915i	0.999315	+	0.0370111i	$0.0117837\pi$
$180$	5.77167	+	8.96358i	0.430195	+	0.668106i
$181$	−0.152251	−	0.263707i	−0.0113168	−	0.0196012i	0.860312	−	0.509769i	$-0.170269\pi$
$181$	−0.152251	−	0.263707i	−0.0113168	−	0.0196012i	−0.871628	+	0.490167i	$0.836936\pi$
$182$	1.14513	−	0.960878i	0.0848827	−	0.0712250i
$183$	5.98466	+	0.906293i	0.442399	+	0.0669951i
$184$	0.0250421	−	0.142021i	0.00184613	−	0.0104699i
$185$	20.6587	+	17.3347i	1.51886	+	1.27448i
$186$	−0.371295	+	1.10257i	−0.0272246	+	0.0808440i
$187$	−4.74712	−	1.72781i	−0.347144	−	0.126350i
$188$	−10.3265			−0.753141
$189$	−0.452971	+	1.59718i	−0.0329488	+	0.116178i
$190$	6.60200			0.478960
$191$	13.5247	+	4.92260i	0.978615	+	0.356187i	0.781301	−	0.624154i	$-0.214556\pi$
$191$	13.5247	+	4.92260i	0.978615	+	0.356187i	0.197313	+	0.980341i	$0.436778\pi$
$192$	1.69795	−	0.342020i	0.122539	−	0.0246832i
$193$	2.33692	+	1.96090i	0.168215	+	0.141149i	0.723009	−	0.690839i	$-0.242759\pi$
$193$	2.33692	+	1.96090i	0.168215	+	0.141149i	−0.554794	+	0.831988i	$0.687203\pi$
$194$	3.24273	−	18.3904i	0.232814	−	1.32036i
$195$	−17.9711	+	22.5030i	−1.28694	+	1.61147i
$196$	−5.28411	+	4.43390i	−0.377437	+	0.316707i
$197$	−11.1321	−	19.2814i	−0.793129	−	1.37374i	−0.924020	−	0.382343i	$-0.875117\pi$
$197$	−11.1321	−	19.2814i	−0.793129	−	1.37374i	0.130891	−	0.991397i	$-0.458216\pi$
$198$	12.7573	+	3.95452i	0.906622	+	0.281036i
$199$	−12.2817	+	21.2725i	−0.870626	+	1.50797i	−0.00927642	+	0.999957i	$0.502953\pi$
$199$	−12.2817	+	21.2725i	−0.870626	+	1.50797i	−0.861350	+	0.508012i	$0.830381\pi$
$200$	1.32470	+	7.51276i	0.0936705	+	0.531232i
$201$	11.3178	+	6.17355i	0.798298	+	0.435449i
$202$	2.27375	−	0.827576i	0.159980	−	0.0582280i
$203$	−1.30878	+	0.476359i	−0.0918587	+	0.0334338i
$204$	1.72538	+	0.941146i	0.120801	+	0.0658934i
$205$	1.34359	+	7.61986i	0.0938402	+	0.532194i
$206$	−0.997676	+	1.72802i	−0.0695114	+	0.120397i
$207$	−0.317552	+	0.293826i	−0.0220714	+	0.0204223i
$208$	2.33937	+	4.05190i	0.162206	+	0.280949i
$209$	6.33595	−	5.31649i	0.438267	−	0.367750i
$210$	−1.22721	+	1.53668i	−0.0846855	+	0.106041i
$211$	−0.524297	+	2.97344i	−0.0360941	+	0.204700i	−0.997522	−	0.0703579i	$-0.977586\pi$
$211$	−0.524297	+	2.97344i	−0.0360941	+	0.204700i	0.961428	+	0.275058i	$0.0886970\pi$
$212$	0.617090	+	0.517800i	0.0423819	+	0.0355627i
$213$	−13.7509	+	2.76987i	−0.942197	+	0.189788i
$214$	−8.33575	−	3.03397i	−0.569820	−	0.207398i
$215$	−25.2230			−1.72019
$216$	−4.67686	−	2.26427i	−0.318220	−	0.154064i
$217$	−0.214606			−0.0145684
$218$	1.85311	+	0.674476i	0.125508	+	0.0456813i
$219$	−8.07124	+	23.9677i	−0.545404	+	1.61959i
$220$	12.1197	+	10.1697i	0.817112	+	0.685638i
$221$	−0.921898	+	5.22835i	−0.0620136	+	0.351697i
$222$	−12.9960	−	1.96806i	−0.872232	−	0.132087i
$223$	7.64543	−	6.41527i	0.511976	−	0.429599i	−0.349848	−	0.936806i	$-0.613767\pi$
$223$	7.64543	−	6.41527i	0.511976	−	0.429599i	0.861824	+	0.507208i	$0.169322\pi$
$224$	0.159750	+	0.276696i	0.0106738	+	0.0184875i
$225$	10.4691	−	20.3510i	0.697940	−	1.35674i
$226$	4.81433	−	8.33866i	0.320244	−	0.554679i
$227$	−3.66786	−	20.8015i	−0.243444	−	1.38064i	−0.824078	−	0.566477i	$-0.808306\pi$
$227$	−3.66786	−	20.8015i	−0.243444	−	1.38064i	0.580633	−	0.814165i	$-0.302805\pi$
$228$	−2.74688	+	1.67596i	−0.181916	+	0.110993i
$229$	21.8767	−	7.96248i	1.44566	−	0.526176i	0.504281	−	0.863539i	$-0.331757\pi$
$229$	21.8767	−	7.96248i	1.44566	−	0.526176i	0.941374	+	0.337364i	$0.109535\pi$
$230$	−0.481576	+	0.175279i	−0.0317542	+	0.0115576i
$231$	0.0597121	+	2.46301i	0.00392877	+	0.162054i
$232$	−0.756973	−	4.29301i	−0.0496977	−	0.281850i
$233$	−13.3621	+	23.1439i	−0.875383	+	1.51621i	−0.0190296	+	0.999819i	$0.506058\pi$
$233$	−13.3621	+	23.1439i	−0.875383	+	1.51621i	−0.856354	+	0.516390i	$0.827276\pi$
$234$	1.76466	−	13.9248i	0.115359	−	0.910295i
$235$	18.3486	+	31.7808i	1.19693	+	2.07315i
$236$	2.28499	−	1.91734i	0.148740	−	0.124808i
$237$	−7.95083	−	20.2998i	−0.516462	−	1.31861i
$238$	−0.0629545	+	0.357033i	−0.00408073	+	0.0231430i
$239$	−18.4309	−	15.4654i	−1.19220	−	1.00037i	−0.999818	−	0.0190518i	$-0.993935\pi$
$239$	−18.4309	−	15.4654i	−1.19220	−	1.00037i	−0.192379	−	0.981321i	$-0.561620\pi$
$240$	−4.06957	−	4.61785i	−0.262690	−	0.298081i
$241$	1.40157	+	0.510130i	0.0902831	+	0.0328604i	0.386767	−	0.922178i	$-0.373592\pi$
$241$	1.40157	+	0.510130i	0.0902831	+	0.0328604i	−0.296484	+	0.955038i	$0.595814\pi$
$242$	8.82079			0.567022
$243$	7.06341	+	13.8963i	0.453118	+	0.891451i
$244$	−3.49464			−0.223721
$245$	23.0347	+	8.38394i	1.47163	+	0.535630i
$246$	−2.49337	−	2.82929i	−0.158972	−	0.180389i
$247$	−6.65855	−	5.58719i	−0.423674	−	0.355504i
$248$	0.116638	−	0.661487i	0.00740653	−	0.0420045i
$249$	−3.41962	−	8.73088i	−0.216710	−	0.553297i
$250$	7.15592	−	6.00453i	0.452580	−	0.379760i
$251$	−7.28748	−	12.6223i	−0.459982	−	0.796711i	0.538978	−	0.842320i	$-0.318811\pi$
$251$	−7.28748	−	12.6223i	−0.459982	−	0.796711i	−0.998959	+	0.0456086i	$0.985477\pi$
$252$	0.120505	−	0.950897i	0.00759107	−	0.0599009i
$253$	−0.321019	+	0.556021i	−0.0201823	+	0.0349568i
$254$	0.0276465	+	0.156791i	0.00173469	+	0.00983794i
$255$	−0.169275	−	6.98226i	−0.0106004	−	0.437246i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	10.3598	−	3.77064i	0.646224	−	0.235206i	0.00194649	−	0.999998i	$-0.499380\pi$
$257$	10.3598	−	3.77064i	0.646224	−	0.235206i	0.644277	+	0.764792i	$0.277158\pi$
$258$	10.4945	−	6.40303i	0.653357	−	0.398635i
$259$	−0.421030	−	2.38778i	−0.0261616	−	0.148370i
$260$	8.31337	−	14.3992i	0.515573	−	0.892999i
$261$	−5.98235	+	11.6292i	−0.370298	+	0.719829i
$262$	4.74292	+	8.21497i	0.293018	+	0.507523i
$263$	−10.0659	+	8.44626i	−0.620688	+	0.520819i	−0.898020	−	0.439955i	$-0.854994\pi$
$263$	−10.0659	+	8.44626i	−0.620688	+	0.520819i	0.277332	+	0.960774i	$0.410550\pi$
$264$	−7.62426	−	1.15459i	−0.469241	−	0.0710599i
$265$	0.497100	−	2.81919i	0.0305366	−	0.173182i
$266$	−0.454698	−	0.381537i	−0.0278793	−	0.0233935i
$267$	−2.79289	+	8.29352i	−0.170922	+	0.507555i
$268$	−6.99437	−	2.54574i	−0.427249	−	0.155506i
$269$	−10.3086			−0.628528			−0.314264	−	0.949336i	$-0.601758\pi$
$269$	−10.3086			−0.628528			−0.314264	+	0.949336i	$0.601758\pi$
$270$	1.34156	+	18.4167i	0.0816448	+	1.12080i
$271$	1.01454			0.0616288			0.0308144	−	0.999525i	$-0.490190\pi$
$271$	1.01454			0.0616288			0.0308144	+	0.999525i	$0.490190\pi$
$272$	−1.06628	−	0.388093i	−0.0646525	−	0.0235316i
$273$	2.53819	−	0.511272i	0.153618	−	0.0309436i
$274$	8.96989	+	7.52663i	0.541891	+	0.454700i
$275$	5.89764	−	33.4472i	0.355641	−	2.01694i
$276$	0.155872	−	0.195179i	0.00938239	−	0.0117484i
$277$	−8.29755	+	6.96247i	−0.498552	+	0.418334i	−0.857079	−	0.515185i	$-0.827723\pi$
$277$	−8.29755	+	6.96247i	−0.498552	+	0.418334i	0.358528	+	0.933519i	$0.383279\pi$
$278$	2.62513	+	4.54686i	0.157445	+	0.272703i
$279$	−1.47906	+	1.36855i	−0.0885488	+	0.0819327i
$280$	0.567702	−	0.983289i	0.0339267	−	0.0587628i
$281$	−1.47197	−	8.34795i	−0.0878103	−	0.497997i	−0.996715	−	0.0809924i	$-0.974191\pi$
$281$	−1.47197	−	8.34795i	−0.0878103	−	0.497997i	0.908904	−	0.417004i	$-0.136920\pi$
$282$	−15.7020	−	8.56501i	−0.935041	−	0.510039i
$283$	−5.92408	+	2.15619i	−0.352150	+	0.128172i	−0.512037	−	0.858963i	$-0.671109\pi$
$283$	−5.92408	+	2.15619i	−0.352150	+	0.128172i	0.159887	+	0.987135i	$0.448887\pi$
$284$	7.61015	−	2.76987i	0.451580	−	0.164362i
$285$	10.0387	+	5.47581i	0.594639	+	0.324359i
$286$	−3.61709	−	20.5135i	−0.213883	−	1.21299i
$287$	0.347824	−	0.602448i	0.0205314	−	0.0355614i
$288$	2.86549	+	0.888246i	0.168850	+	0.0523404i
$289$	7.85622	+	13.6074i	0.462130	+	0.800434i
$290$	−11.8671	+	9.95764i	−0.696857	+	0.584733i
$291$	20.1840	−	25.2740i	1.18321	−	1.48159i
$292$	2.53549	−	14.3795i	0.148378	−	0.841495i
$293$	−1.86383	−	1.56394i	−0.108886	−	0.0913662i	0.586719	−	0.809790i	$-0.300419\pi$
$293$	−1.86383	−	1.56394i	−0.108886	−	0.0913662i	−0.695605	+	0.718424i	$0.744864\pi$
$294$	−11.7123	+	2.35923i	−0.683075	+	0.137593i
$295$	−9.96083	−	3.62544i	−0.579942	−	0.211082i
$296$	7.58877			0.441088
$297$	16.1182	+	16.5942i	0.935271	+	0.962891i
$298$	−16.2922			−0.943784
$299$	0.634037	+	0.230771i	0.0366673	+	0.0133458i
$300$	−4.21693	+	12.5222i	−0.243465	+	0.722972i
$301$	1.73718	+	1.45767i	0.100129	+	0.0840184i
$302$	−2.71203	+	15.3807i	−0.156060	+	0.885058i
$303$	4.14375	+	0.627512i	0.238052	+	0.0360496i
$304$	1.42315	−	1.19417i	0.0816233	−	0.0684901i
$305$	6.20942	+	10.7550i	0.355550	+	0.615831i
$306$	1.84292	+	2.86212i	0.105353	+	0.163616i
$307$	11.8629	−	20.5471i	0.677050	−	1.17269i	−0.298815	−	0.954311i	$-0.596591\pi$
$307$	11.8629	−	20.5471i	0.677050	−	1.17269i	0.975865	−	0.218374i	$-0.0700754\pi$
$308$	−0.247003	−	1.40083i	−0.0140743	−	0.0798194i
$309$	−2.95027	+	1.80006i	−0.167835	+	0.102402i
$310$	−2.24303	+	0.816395i	−0.127395	+	0.0463681i
$311$	10.1493	−	3.69403i	0.575511	−	0.209469i	−0.0378338	−	0.999284i	$-0.512046\pi$
$311$	10.1493	−	3.69403i	0.575511	−	0.209469i	0.613345	+	0.789815i	$0.289824\pi$
$312$	0.196408	+	8.10143i	0.0111194	+	0.458653i
$313$	−2.75948	−	15.6498i	−0.155975	−	0.884577i	−0.957889	−	0.287138i	$-0.907296\pi$
$313$	−2.75948	−	15.6498i	−0.155975	−	0.884577i	0.801914	−	0.597439i	$-0.203815\pi$
$314$	−8.81577	+	15.2694i	−0.497503	+	0.861700i
$315$	−3.14058	+	1.31873i	−0.176952	+	0.0743021i
$316$	6.29350	+	10.9007i	0.354037	+	0.613210i
$317$	−2.47819	+	2.07944i	−0.139189	+	0.116793i	−0.709724	−	0.704480i	$-0.751180\pi$
$317$	−2.47819	+	2.07944i	−0.139189	+	0.116793i	0.570535	+	0.821273i	$0.306736\pi$
$318$	0.508844	+	1.29917i	0.0285346	+	0.0728536i
$319$	−3.37009	+	19.1127i	−0.188689	+	1.07011i
$320$	2.72228	+	2.28426i	0.152180	+	0.127694i
$321$	−10.1585	−	11.5271i	−0.566992	−	0.643380i
$322$	0.0432970	+	0.0157588i	0.00241285	+	0.000878205i
$323$	2.10805			0.117295
$324$	−5.23337	−	7.32201i	−0.290743	−	0.406778i
$325$	−35.6925			−1.97986
$326$	14.9224	+	5.43131i	0.826475	+	0.300812i
$327$	2.25832	+	2.56257i	0.124885	+	0.141711i
$328$	1.66790	+	1.39954i	0.0920946	+	0.0772765i
$329$	0.572924	−	3.24922i	0.0315863	−	0.179135i
$330$	9.99376	+	25.5158i	0.550138	+	1.40460i
$331$	−13.5311	+	11.3540i	−0.743739	+	0.624071i	−0.933839	−	0.357693i	$-0.883563\pi$
$331$	−13.5311	+	11.3540i	−0.743739	+	0.624071i	0.190100	+	0.981765i	$0.439119\pi$
$332$	2.70681	+	4.68834i	0.148556	+	0.257306i
$333$	−18.1287	−	13.7716i	−0.993444	−	0.754678i
$334$	6.78921	−	11.7593i	0.371489	−	0.643438i
$335$	4.59316	+	26.0491i	0.250951	+	1.42321i
$336$	0.0134123	+	0.553229i	0.000731699	+	0.0301811i
$337$	9.90706	−	3.60588i	0.539672	−	0.196425i	−0.0577798	−	0.998329i	$-0.518402\pi$
$337$	9.90706	−	3.60588i	0.539672	−	0.196425i	0.597452	+	0.801905i	$0.296180\pi$
$338$	−8.35441	+	3.04076i	−0.454420	+	0.165395i
$339$	14.2366	−	8.68625i	0.773228	−	0.471773i
$340$	0.700218	+	3.97113i	0.0379746	+	0.215365i
$341$	−1.49520	+	2.58977i	−0.0809699	+	0.140244i
$342$	−5.56683	+	0.270079i	−0.301020	+	0.0146042i
$343$	−2.22020	−	3.84550i	−0.119879	−	0.207637i
$344$	−5.43716	+	4.56232i	−0.293152	+	0.245984i
$345$	−0.877639	−	0.132906i	−0.0472505	−	0.00715543i
$346$	1.11906	−	6.34650i	0.0601610	−	0.341190i
$347$	24.9000	+	20.8936i	1.33670	+	1.12163i	0.982460	+	0.186473i	$0.0597058\pi$
$347$	24.9000	+	20.8936i	1.33670	+	1.12163i	0.354243	+	0.935153i	$0.384739\pi$
$348$	2.40968	−	7.15558i	0.129172	−	0.383579i
$349$	18.8599	+	6.86444i	1.00955	+	0.367445i	0.793259	−	0.608884i	$-0.208383\pi$
$349$	18.8599	+	6.86444i	1.00955	+	0.367445i	0.216289	+	0.976329i	$0.430605\pi$
$350$	−2.43736			−0.130282
$351$	14.2327	−	19.7098i	0.759687	−	1.05203i
$352$	4.45206			0.237295
$353$	−10.3705	−	3.77455i	−0.551966	−	0.200899i	0.0509539	−	0.998701i	$-0.483774\pi$
$353$	−10.3705	−	3.77455i	−0.551966	−	0.200899i	−0.602920	+	0.797802i	$0.705996\pi$
$354$	5.06472	−	1.02019i	0.269187	−	0.0542227i
$355$	−22.0465	−	18.4992i	−1.17011	−	0.981837i
$356$	0.877354	−	4.97572i	0.0464997	−	0.263713i
$357$	−0.391854	+	0.490670i	−0.0207391	+	0.0259690i
$358$	−9.58494	+	8.04272i	−0.506580	+	0.425071i
$359$	1.96044	+	3.39557i	0.103468	+	0.179212i	0.913111	−	0.407711i	$-0.133673\pi$
$359$	1.96044	+	3.39557i	0.103468	+	0.179212i	−0.809643	+	0.586922i	$0.800339\pi$
$360$	−2.35787	−	10.3970i	−0.124271	−	0.547972i
$361$	7.77430	−	13.4655i	0.409174	−	0.708710i
$362$	0.0528764	+	0.299877i	0.00277912	+	0.0157612i
$363$	13.4124	+	7.31611i	0.703971	+	0.383996i
$364$	−1.40471	+	0.511272i	−0.0736268	+	0.0267980i
$365$	−48.7591	+	17.7469i	−2.55217	+	0.928914i
$366$	−5.31377	−	2.89851i	−0.277755	−	0.151508i
$367$	5.06206	+	28.7084i	0.264237	+	1.49856i	0.771198	+	0.636595i	$0.219658\pi$
$367$	5.06206	+	28.7084i	0.264237	+	1.49856i	−0.506961	+	0.861969i	$0.669231\pi$
$368$	−0.0721058	+	0.124891i	−0.00375878	+	0.00651039i
$369$	−1.44463	−	6.37013i	−0.0752047	−	0.331615i
$370$	−13.4840	−	23.3550i	−0.701001	−	1.21417i
$371$	−0.197161	+	0.165438i	−0.0102361	+	0.00858909i
$372$	0.726002	−	0.909082i	0.0376415	−	0.0471337i
$373$	1.08909	−	6.17653i	0.0563909	−	0.319809i	−0.943544	−	0.331248i	$-0.892530\pi$
$373$	1.08909	−	6.17653i	0.0563909	−	0.319809i	0.999935	+	0.0114395i	$0.00364140\pi$
$374$	3.86989	+	3.24722i	0.200107	+	0.167910i
$375$	15.8612	−	3.19494i	0.819068	−	0.164986i
$376$	9.70378	+	3.53189i	0.500434	+	0.182143i
$377$	20.3957			1.05043
$378$	0.971923	−	1.34594i	0.0499903	−	0.0692276i
$379$	−26.9562			−1.38465			−0.692324	−	0.721587i	$-0.743413\pi$
$379$	−26.9562			−1.38465			−0.692324	+	0.721587i	$0.743413\pi$
$380$	−6.20385	−	2.25802i	−0.318251	−	0.115834i
$381$	−0.0880072	+	0.261339i	−0.00450874	+	0.0133888i
$382$	−11.0255	−	9.25146i	−0.564111	−	0.473346i
$383$	−0.565446	+	3.20680i	−0.0288929	+	0.163860i	−0.995840	−	0.0911163i	$-0.970957\pi$
$383$	−0.565446	+	3.20680i	−0.0288929	+	0.163860i	0.966947	+	0.254976i	$0.0820676\pi$
$384$	−1.71253	−	0.259338i	−0.0873920	−	0.0132343i
$385$	−3.87226	+	3.24922i	−0.197349	+	0.165595i
$386$	−1.52531	−	2.64192i	−0.0776364	−	0.134470i
$387$	21.2681	−	1.03184i	1.08112	−	0.0524512i
$388$	−9.33706	+	16.1723i	−0.474018	+	0.821022i
$389$	0.241315	+	1.36857i	0.0122352	+	0.0693891i	0.990314	−	0.138846i	$-0.0443392\pi$
$389$	0.241315	+	1.36857i	0.0122352	+	0.0693891i	−0.978079	+	0.208235i	$0.933228\pi$
$390$	24.5838	−	14.9994i	1.24485	−	0.759525i
$391$	−0.153770	+	0.0559675i	−0.00777646	+	0.00283040i
$392$	6.48192	−	2.35923i	0.327387	−	0.119159i
$393$	0.398204	+	16.4251i	0.0200867	+	0.828538i
$394$	3.86614	+	21.9260i	0.194773	+	1.10461i
$395$	22.3651	−	38.7375i	1.12531	−	1.94909i
$396$	−10.6354	−	8.07929i	−0.534450	−	0.406000i
$397$	−1.07010	−	1.85347i	−0.0537069	−	0.0930230i	0.837922	−	0.545790i	$-0.183770\pi$
$397$	−1.07010	−	1.85347i	−0.0537069	−	0.0930230i	−0.891629	+	0.452767i	$0.850437\pi$
$398$	18.8167	−	15.7890i	0.943193	−	0.791433i
$399$	−0.374938	−	0.957280i	−0.0187704	−	0.0479239i
$400$	1.32470	−	7.51276i	0.0662351	−	0.375638i
$401$	−6.55222	−	5.49796i	−0.327202	−	0.274555i	0.464357	−	0.885648i	$-0.346286\pi$
$401$	−6.55222	−	5.49796i	−0.327202	−	0.274555i	−0.791559	+	0.611093i	$0.790730\pi$
$402$	−8.52379	−	9.67216i	−0.425128	−	0.482404i
$403$	2.95314	+	1.07486i	0.147107	+	0.0535424i
$404$	−2.41967			−0.120383
$405$	−13.2352	+	29.1162i	−0.657661	+	1.44679i
$406$	1.39278			0.0691225
$407$	−31.7481	−	11.5554i	−1.57369	−	0.572778i
$408$	−1.29944	−	1.47450i	−0.0643316	−	0.0729987i
$409$	20.8915	+	17.5300i	1.03302	+	0.866804i	0.991207	−	0.132322i	$-0.0422433\pi$
$409$	20.8915	+	17.5300i	1.03302	+	0.866804i	0.0418096	+	0.999126i	$0.486688\pi$
$410$	1.34359	−	7.61986i	0.0663550	−	0.376318i
$411$	7.39644	+	18.8844i	0.364840	+	0.931498i
$412$	1.52853	−	1.28259i	0.0753052	−	0.0631885i
$413$	0.476511	+	0.825342i	0.0234476	+	0.0406124i
$414$	0.398896	−	0.167497i	0.0196047	−	0.00823201i
$415$	9.61916	−	16.6609i	0.472186	−	0.817850i
$416$	−0.812454	−	4.60766i	−0.0398338	−	0.225909i
$417$	0.220400	+	9.09106i	0.0107930	+	0.445191i
$418$	−7.77219	+	2.82885i	−0.380150	+	0.138363i
$419$	−15.0495	+	5.47757i	−0.735216	+	0.267597i	−0.682371	−	0.731006i	$-0.739051\pi$
$419$	−15.0495	+	5.47757i	−0.735216	+	0.267597i	−0.0528448	+	0.998603i	$0.516829\pi$
$420$	1.67877	−	1.02428i	0.0819158	−	0.0499796i
$421$	−3.15120	−	17.8713i	−0.153580	−	0.870995i	−0.960073	−	0.279751i	$-0.909748\pi$
$421$	−3.15120	−	17.8713i	−0.153580	−	0.870995i	0.806493	−	0.591244i	$-0.201363\pi$
$422$	1.50965	−	2.61480i	0.0734888	−	0.127286i
$423$	−16.7717	−	26.0470i	−0.815469	−	1.26645i
$424$	−0.402777	−	0.697630i	−0.0195606	−	0.0338799i
$425$	6.63111	−	5.56416i	0.321656	−	0.269901i
$426$	13.8690	+	2.10026i	0.671954	+	0.101758i
$427$	0.193885	−	1.09958i	0.00938276	−	0.0532123i
$428$	6.79537	+	5.70199i	0.328467	+	0.275616i
$429$	11.5143	−	34.1919i	0.555916	−	1.65080i
$430$	23.7019	+	8.62677i	1.14301	+	0.416020i
$431$	2.13698			0.102935			0.0514673	−	0.998675i	$-0.483610\pi$
$431$	2.13698			0.102935			0.0514673	+	0.998675i	$0.483610\pi$
$432$	3.62039	+	3.72730i	0.174186	+	0.179330i
$433$	25.1733			1.20975			0.604876	−	0.796320i	$-0.293223\pi$
$433$	25.1733			1.20975			0.604876	+	0.796320i	$0.293223\pi$
$434$	0.201664	+	0.0733996i	0.00968017	+	0.00352329i
$435$	−26.3035	+	5.29835i	−1.26115	+	0.254036i
$436$	−1.51067	−	1.26760i	−0.0723478	−	0.0607071i
$437$	0.0465230	−	0.263845i	0.00222550	−	0.0126214i
$438$	15.7819	−	19.7617i	0.754089	−	0.944252i
$439$	19.8037	−	16.6173i	0.945179	−	0.793099i	−0.0333002	−	0.999445i	$-0.510602\pi$
$439$	19.8037	−	16.6173i	0.945179	−	0.793099i	0.978479	+	0.206346i	$0.0661573\pi$
$440$	−7.91059	−	13.7015i	−0.377123	−	0.653196i
$441$	−19.7659	−	6.12705i	−0.941233	−	0.291764i
$442$	2.65450	−	4.59773i	0.126262	−	0.218692i
$443$	2.42041	+	13.7268i	0.114997	+	0.652181i	0.986752	+	0.162238i	$0.0518713\pi$
$443$	2.42041	+	13.7268i	0.114997	+	0.652181i	−0.871755	+	0.489943i	$0.837018\pi$
$444$	11.5391	+	6.29425i	0.547621	+	0.298712i
$445$	−16.8721	+	6.14094i	−0.799814	+	0.291108i
$446$	−9.37850	+	3.41350i	−0.444085	+	0.161634i
$447$	−24.7731	−	13.5131i	−1.17173	−	0.639145i
$448$	−0.0554807	−	0.314647i	−0.00262122	−	0.0148657i
$449$	−14.5769	+	25.2479i	−0.687927	+	1.19152i	0.284581	+	0.958652i	$0.408146\pi$
$449$	−14.5769	+	25.2479i	−0.687927	+	1.19152i	−0.972507	+	0.232872i	$0.925188\pi$
$450$	−16.7982	+	15.5431i	−0.791875	+	0.732708i
$451$	−4.84672	−	8.39476i	−0.228223	−	0.395294i
$452$	−7.37598	+	6.18918i	−0.346937	+	0.291114i
$453$	−16.8807	+	21.1376i	−0.793126	+	0.993133i
$454$	−3.66786	+	20.8015i	−0.172141	+	0.976261i
$455$	4.06943	+	3.41465i	0.190778	+	0.160081i
$456$	3.15443	−	0.635402i	0.147720	−	0.0297554i
$457$	−22.3630	−	8.13945i	−1.04609	−	0.380747i	−0.238907	−	0.971042i	$-0.576789\pi$
$457$	−22.3630	−	8.13945i	−1.04609	−	0.380747i	−0.807188	+	0.590295i	$0.799011\pi$
$458$	−23.2807			−1.08784
$459$	0.428367	+	5.88054i	0.0199945	+	0.274480i
$460$	0.512482			0.0238946
$461$	−28.9550	−	10.5388i	−1.34857	−	0.490839i	−0.436069	−	0.899913i	$-0.643630\pi$
$461$	−28.9550	−	10.5388i	−1.34857	−	0.490839i	−0.912501	+	0.409074i	$0.865852\pi$
$462$	0.786287	−	2.33489i	0.0365814	−	0.108629i
$463$	27.6849	+	23.2304i	1.28663	+	1.07961i	0.992294	+	0.123907i	$0.0395424\pi$
$463$	27.6849	+	23.2304i	1.28663	+	1.07961i	0.294334	+	0.955703i	$0.404902\pi$
$464$	−0.756973	+	4.29301i	−0.0351416	+	0.199298i
$465$	−4.08776	−	0.619035i	−0.189565	−	0.0287070i
$466$	20.4720	−	17.1780i	0.948347	−	0.795758i
$467$	18.4877	+	32.0217i	0.855509	+	1.48179i	0.876172	+	0.481999i	$0.160089\pi$
$467$	18.4877	+	32.0217i	0.855509	+	1.48179i	−0.0206626	+	0.999787i	$0.506578\pi$
$468$	−6.42081	+	12.4815i	−0.296802	+	0.576959i
$469$	1.18906	−	2.05952i	0.0549058	−	0.0950996i
$470$	−6.37241	−	36.1397i	−0.293937	−	1.66700i
$471$	−26.0695	+	15.9059i	−1.20122	+	0.732904i
$472$	−2.80296	+	1.02019i	−0.129017	+	0.0469582i
$473$	29.6937	−	10.8076i	1.36532	−	0.496935i
$474$	0.528387	+	21.7949i	0.0242696	+	1.00107i
$475$	2.46102	+	13.9571i	0.112919	+	0.640398i
$476$	0.181270	−	0.313969i	0.00830850	−	0.0143908i
$477$	−0.303827	+	2.39749i	−0.0139113	+	0.109773i
$478$	12.0299	+	20.8365i	0.550236	+	0.953037i
$479$	29.4015	−	24.6708i	1.34339	−	1.12724i	0.362647	−	0.931926i	$-0.381873\pi$
$479$	29.4015	−	24.6708i	1.34339	−	1.12724i	0.980741	−	0.195311i	$-0.0625715\pi$
$480$	2.24475	+	5.73123i	0.102458	+	0.261594i
$481$	−6.16553	+	34.9664i	−0.281124	+	1.59433i
$482$	−1.14257	−	0.958731i	−0.0520427	−	0.0436690i
$483$	0.0527646	+	0.0598733i	0.00240087	+	0.00272433i
$484$	−8.28884	−	3.01689i	−0.376765	−	0.137131i
$485$	66.3619			3.01334
$486$	−1.88461	−	15.4741i	−0.0854876	−	0.701920i
$487$	34.3088			1.55468			0.777339	−	0.629082i	$-0.216569\pi$
$487$	34.3088			1.55468			0.777339	+	0.629082i	$0.216569\pi$
$488$	3.28389	+	1.19524i	0.148655	+	0.0541059i
$489$	18.1854	+	20.6354i	0.822373	+	0.933167i
$490$	−18.7781	−	15.7567i	−0.848306	−	0.711813i
$491$	−3.02281	+	17.1432i	−0.136417	+	0.773661i	0.837445	+	0.546522i	$0.184048\pi$
$491$	−3.02281	+	17.1432i	−0.136417	+	0.773661i	−0.973862	+	0.227139i	$0.927063\pi$
$492$	1.37533	+	3.51145i	0.0620046	+	0.158308i
$493$	−3.78921	+	3.17952i	−0.170657	+	0.143199i
$494$	4.34606	+	7.52760i	0.195539	+	0.338683i
$495$	−5.96720	+	47.0870i	−0.268206	+	2.11640i
$496$	−0.335846	+	0.581702i	−0.0150799	+	0.0261192i
$497$	0.449314	+	2.54819i	0.0201545	+	0.114302i
$498$	0.227258	+	9.37392i	0.0101837	+	0.420056i
$499$	−24.6982	+	8.98939i	−1.10564	+	0.402421i	−0.829393	−	0.558666i	$-0.811313\pi$
$499$	−24.6982	+	8.98939i	−1.10564	+	0.402421i	−0.276248	+	0.961086i	$0.589091\pi$
$500$	−8.77804	+	3.19494i	−0.392566	+	0.142882i
$501$	20.0766	−	12.2494i	0.896958	−	0.547265i
$502$	2.53091	+	14.3535i	0.112960	+	0.640629i
$503$	9.08930	−	15.7431i	0.405272	−	0.701952i	−0.589081	−	0.808074i	$-0.700510\pi$
$503$	9.08930	−	15.7431i	0.405272	−	0.701952i	0.994353	+	0.106122i	$0.0338435\pi$
$504$	−0.438463	+	0.852336i	−0.0195307	+	0.0379661i
$505$	4.29937	+	7.44672i	0.191319	+	0.331375i
$506$	0.491830	−	0.412694i	0.0218645	−	0.0183465i
$507$	−15.2253	−	2.30567i	−0.676181	−	0.102398i
$508$	0.0276465	−	0.156791i	0.00122661	−	0.00695647i
$509$	−18.8746	−	15.8376i	−0.836600	−	0.701991i	0.120196	−	0.992750i	$-0.461648\pi$
$509$	−18.8746	−	15.8376i	−0.836600	−	0.701991i	−0.956796	+	0.290759i	$0.906092\pi$
$510$	−2.22901	+	6.61907i	−0.0987020	+	0.293097i
$511$	4.38379	+	1.59557i	0.193927	+	0.0705838i
$512$	1.00000			0.0441942
$513$	−8.68864	−	4.20655i	−0.383613	−	0.185724i
$514$	−11.0246			−0.486275
$515$	−6.66321	−	2.42521i	−0.293616	−	0.106868i
$516$	−12.0515	+	2.42756i	−0.530539	+	0.106867i
$517$	−35.2184	−	29.5517i	−1.54890	−	1.29968i
$518$	−0.421030	+	2.38778i	−0.0184990	+	0.104913i
$519$	6.96548	−	8.72200i	0.305750	−	0.382853i
$520$	−12.7368	+	10.6875i	−0.558547	+	0.468676i
$521$	−15.0065	−	25.9921i	−0.657449	−	1.13873i	−0.981274	−	0.192618i	$-0.938302\pi$
$521$	−15.0065	−	25.9921i	−0.657449	−	1.13873i	0.323825	−	0.946117i	$-0.395031\pi$
$522$	9.59898	−	8.88178i	0.420136	−	0.388745i
$523$	13.6719	−	23.6804i	0.597829	−	1.03547i	−0.395312	−	0.918547i	$-0.629363\pi$
$523$	13.6719	−	23.6804i	0.597829	−	1.03547i	0.993141	−	0.116924i	$-0.0373033\pi$
$524$	−1.64720	−	9.34172i	−0.0719582	−	0.408095i
$525$	−3.70613	−	2.02159i	−0.161749	−	0.0882293i
$526$	12.3476	−	4.49416i	0.538381	−	0.195955i
$527$	−0.716210	+	0.260679i	−0.0311986	+	0.0113554i
$528$	6.76957	+	3.69261i	0.294608	+	0.160700i
$529$	−3.99030	−	22.6301i	−0.173491	−	0.983917i
$530$	−1.43134	+	2.47916i	−0.0621735	+	0.107688i
$531$	8.54731	+	2.64950i	0.370922	+	0.114979i
$532$	0.296783	+	0.514044i	0.0128672	+	0.0222866i
$533$	−7.80368	+	6.54807i	−0.338015	+	0.283628i
$534$	5.46100	−	6.83814i	0.236321	−	0.295915i
$535$	5.47404	−	31.0448i	0.236663	−	1.34218i
$536$	5.70186	+	4.78443i	0.246283	+	0.206656i
$537$	−21.2451	+	4.27944i	−0.916795	+	0.184672i
$538$	9.68695	+	3.52576i	0.417634	+	0.152006i
$539$	−30.7099			−1.32277
$540$	5.03822	−	17.7649i	0.216810	−	0.764478i
$541$	8.65632			0.372164			0.186082	−	0.982534i	$-0.440421\pi$
$541$	8.65632			0.372164			0.186082	+	0.982534i	$0.440421\pi$
$542$	−0.953353	−	0.346992i	−0.0409500	−	0.0149046i
$543$	−0.168322	+	0.499834i	−0.00722337	+	0.0214499i
$544$	0.869237	+	0.729376i	0.0372682	+	0.0312718i
$545$	−1.21692	+	6.90152i	−0.0521273	+	0.295629i
$546$	−2.55999	−	0.387674i	−0.109557	−	0.0165909i
$547$	21.1005	−	17.7055i	0.902194	−	0.757031i	−0.0684237	−	0.997656i	$-0.521797\pi$
$547$	21.1005	−	17.7055i	0.902194	−	0.757031i	0.970618	+	0.240625i	$0.0773525\pi$
$548$	−5.85468	−	10.1406i	−0.250100	−	0.433185i
$549$	−5.67577	−	8.81466i	−0.242236	−	0.376200i
$550$	−16.9816	+	29.4130i	−0.724097	+	1.25417i
$551$	−1.40630	−	7.97552i	−0.0599104	−	0.339769i
$552$	−0.213227	+	0.130097i	−0.00907554	+	0.00553730i
$553$	−3.77903	+	1.37545i	−0.160701	+	0.0584903i
$554$	10.1785	−	3.70465i	0.432441	−	0.157396i
$555$	−1.13209	−	46.6963i	−0.0480544	−	1.98215i
$556$	−0.911699	−	5.17050i	−0.0386647	−	0.219278i
$557$	13.0903	−	22.6730i	0.554653	−	0.960687i	−0.443278	−	0.896384i	$-0.646184\pi$
$557$	13.0903	−	22.6730i	0.554653	−	0.960687i	0.997930	−	0.0643022i	$-0.0204822\pi$
$558$	1.85793	−	0.780146i	0.0786524	−	0.0330262i
$559$	−16.6042	−	28.7592i	−0.702281	−	1.21639i
$560$	−0.869770	+	0.729824i	−0.0367545	+	0.0308407i
$561$	3.19106	+	8.14731i	0.134727	+	0.343980i
$562$	−1.47197	+	8.34795i	−0.0620912	+	0.352137i
$563$	−3.04293	−	2.55332i	−0.128244	−	0.107610i	0.576410	−	0.817161i	$-0.304453\pi$
$563$	−3.04293	−	2.55332i	−0.128244	−	0.107610i	−0.704654	+	0.709551i	$0.748898\pi$
$564$	11.8257	+	13.4189i	0.497950	+	0.565037i
$565$	32.1536	+	11.7030i	1.35271	+	0.492347i
$566$	6.30428			0.264988
$567$	2.59420	−	1.24043i	0.108946	−	0.0520934i
$568$	−8.09856			−0.339808
$569$	38.0492	+	13.8488i	1.59511	+	0.580571i	0.978418	−	0.206636i	$-0.0662516\pi$
$569$	38.0492	+	13.8488i	1.59511	+	0.580571i	0.616688	+	0.787207i	$0.288474\pi$
$570$	−7.56043	−	8.57900i	−0.316671	−	0.359335i
$571$	29.3406	+	24.6197i	1.22787	+	1.03030i	0.998375	+	0.0569933i	$0.0181514\pi$
$571$	29.3406	+	24.6197i	1.22787	+	1.03030i	0.229493	+	0.973310i	$0.426293\pi$
$572$	−3.61709	+	20.5135i	−0.151238	+	0.857714i
$573$	−9.09143	−	23.2120i	−0.379800	−	0.969694i
$574$	−0.532897	+	0.447153i	−0.0222427	+	0.0186638i
$575$	−0.550070	−	0.952749i	−0.0229395	−	0.0397324i
$576$	−2.38888	−	1.81473i	−0.0995366	−	0.0756139i
$577$	−4.13928	+	7.16944i	−0.172320	+	0.298468i	−0.939231	−	0.343287i	$-0.888460\pi$
$577$	−4.13928	+	7.16944i	−0.172320	+	0.298468i	0.766910	+	0.641754i	$0.221793\pi$
$578$	−2.72844	−	15.4737i	−0.113488	−	0.643622i
$579$	−0.128062	−	5.28229i	−0.00532206	−	0.219524i
$580$	14.5571	−	5.29835i	0.604450	−	0.220002i
$581$	−1.62535	+	0.591578i	−0.0674308	+	0.0245428i
$582$	−27.6110	+	16.8464i	−1.14451	+	0.698306i
$583$	0.622767	+	3.53189i	0.0257924	+	0.146276i
$584$	−7.30065	+	12.6451i	−0.302103	+	0.523258i
$585$	49.8216	−	2.41713i	2.05987	−	0.0999360i
$586$	1.21653	+	2.10709i	0.0502543	+	0.0870430i
$587$	−10.6808	+	8.96228i	−0.440845	+	0.369913i	−0.836025	−	0.548691i	$-0.815126\pi$
$587$	−10.6808	+	8.96228i	−0.440845	+	0.369913i	0.395181	+	0.918603i	$0.370682\pi$
$588$	11.8129	+	1.78889i	0.487154	+	0.0737727i
$589$	0.216689	−	1.22891i	0.00892853	−	0.0506362i
$590$	8.12014	+	6.81361i	0.334301	+	0.280512i
$591$	−12.3071	+	36.5461i	−0.506246	+	1.50331i
$592$	−7.13111	−	2.59551i	−0.293087	−	0.106675i
$593$	−41.2342			−1.69329			−0.846644	−	0.532160i	$-0.821380\pi$
$593$	−41.2342			−1.69329			−0.846644	+	0.532160i	$0.821380\pi$
$594$	−9.47058	−	21.1061i	−0.388583	−	0.865996i
$595$	−1.28835			−0.0528173
$596$	15.3097	+	5.57227i	0.627110	+	0.228249i
$597$	41.7073	−	8.40117i	1.70697	−	0.343837i
$598$	−0.516872	−	0.433707i	−0.0211365	−	0.0177356i
$599$	−0.544602	+	3.08859i	−0.0222518	+	0.126196i	−0.993910	−	0.110193i	$-0.964853\pi$
$599$	−0.544602	+	3.08859i	−0.0222518	+	0.126196i	0.971658	+	0.236390i	$0.0759641\pi$
$600$	8.24548	−	10.3248i	0.336620	−	0.421507i
$601$	−26.6855	+	22.3918i	−1.08853	+	0.913382i	−0.996601	−	0.0823839i	$-0.973747\pi$
$601$	−26.6855	+	22.3918i	−1.08853	+	0.913382i	−0.0919256	+	0.995766i	$0.529302\pi$
$602$	−1.13386	−	1.96391i	−0.0462128	−	0.0800429i
$603$	−4.93859	−	21.7768i	−0.201115	−	0.886819i
$604$	7.80897	−	13.5255i	0.317742	−	0.550346i
$605$	5.44323	+	30.8701i	0.221299	+	1.25505i
$606$	−3.67923	−	2.00691i	−0.149458	−	0.0815253i
$607$	0.726574	−	0.264451i	0.0294907	−	0.0107338i	−0.327233	−	0.944944i	$-0.606116\pi$
$607$	0.726574	−	0.264451i	0.0294907	−	0.0107338i	0.356723	+	0.934210i	$0.383894\pi$
$608$	−1.74575	+	0.635402i	−0.0707997	+	0.0257690i
$609$	2.11779	+	1.15519i	0.0858172	+	0.0468108i
$610$	−2.15651	−	12.2302i	−0.0873145	−	0.495185i
$611$	−24.1576	+	41.8422i	−0.977312	+	1.69275i
$612$	−0.752879	−	3.31983i	−0.0304333	−	0.134196i
$613$	−6.99919	−	12.1230i	−0.282695	−	0.489642i	0.689353	−	0.724426i	$-0.257895\pi$
$613$	−6.99919	−	12.1230i	−0.282695	−	0.489642i	−0.972048	+	0.234784i	$0.924562\pi$
$614$	−18.1750	+	15.2506i	−0.733483	+	0.615465i
$615$	8.36302	−	10.4720i	0.337230	−	0.422271i
$616$	−0.247003	+	1.40083i	−0.00995205	+	0.0564409i
$617$	8.97302	+	7.52926i	0.361240	+	0.303117i	0.805285	−	0.592888i	$-0.202012\pi$
$617$	8.97302	+	7.52926i	0.361240	+	0.303117i	−0.444045	+	0.896005i	$0.646457\pi$
$618$	3.38800	−	0.682450i	0.136285	−	0.0274522i
$619$	−45.1425	−	16.4305i	−1.81443	−	0.660398i	−0.996357	−	0.0852845i	$-0.972820\pi$
$619$	−45.1425	−	16.4305i	−1.81443	−	0.660398i	−0.818073	−	0.575114i	$-0.804958\pi$
$620$	2.38698			0.0958634
$621$	0.745465	+	0.0761639i	0.0299145	+	0.00305635i
$622$	−10.8006			−0.433065
$623$	1.51692	+	0.552114i	0.0607741	+	0.0221200i
$624$	2.58629	−	7.68003i	0.103534	−	0.307447i
$625$	−3.78956	−	3.17982i	−0.151583	−	0.127193i
$626$	−2.75948	+	15.6498i	−0.110291	+	0.625490i
$627$	−14.1643	−	2.14498i	−0.565667	−	0.0856624i
$628$	13.5065	−	11.3333i	0.538970	−	0.452249i
$629$	−4.30552	−	7.45738i	−0.171672	−	0.297345i
$630$	3.40221	−	0.165061i	0.135547	−	0.00657617i
$631$	−19.7725	+	34.2469i	−0.787130	+	1.36335i	0.140589	+	0.990068i	$0.455100\pi$
$631$	−19.7725	+	34.2469i	−0.787130	+	1.36335i	−0.927719	+	0.373280i	$0.878233\pi$
$632$	−2.18571	−	12.3958i	−0.0869429	−	0.493078i
$633$	4.46426	−	2.72379i	0.177438	−	0.108261i
$634$	3.03994	−	1.10645i	0.120732	−	0.0439427i
$635$	−0.531660	+	0.193508i	−0.0210983	+	0.00767915i
$636$	−0.0338162	−	1.39485i	−0.00134090	−	0.0553094i
$637$	5.60424	+	31.7832i	0.222048	+	1.25930i
$638$	9.70378	−	16.8074i	0.384176	−	0.665413i
$639$	19.3465	+	14.6967i	0.765335	+	0.581393i
$640$	−1.77684	−	3.07758i	−0.0702358	−	0.121652i
$641$	0.506596	−	0.425085i	0.0200093	−	0.0167898i	−0.632728	−	0.774374i	$-0.718065\pi$
$641$	0.506596	−	0.425085i	0.0200093	−	0.0167898i	0.652737	+	0.757584i	$0.273620\pi$
$642$	5.60336	+	14.3063i	0.221147	+	0.564626i
$643$	0.314901	−	1.78589i	0.0124185	−	0.0704288i	−0.977969	−	0.208752i	$-0.933060\pi$
$643$	0.314901	−	1.78589i	0.0124185	−	0.0704288i	0.990387	+	0.138323i	$0.0441711\pi$
$644$	−0.0352961	−	0.0296169i	−0.00139086	−	0.00116707i
$645$	28.8847	+	32.7761i	1.13733	+	1.29056i
$646$	−1.98092	−	0.720997i	−0.0779383	−	0.0283672i
$647$	4.13765			0.162668			0.0813339	−	0.996687i	$-0.474082\pi$
$647$	4.13765			0.162668			0.0813339	+	0.996687i	$0.474082\pi$
$648$	2.41349	+	8.67036i	0.0948108	+	0.340604i
$649$	13.2798			0.521278
$650$	33.5399	+	12.2075i	1.31554	+	0.478819i
$651$	0.245761	+	0.278871i	0.00963213	+	0.0109298i
$652$	−12.1648	−	10.2075i	−0.476412	−	0.399757i
$653$	4.66662	−	26.4657i	0.182619	−	1.03568i	−0.746357	−	0.665545i	$-0.768199\pi$
$653$	4.66662	−	26.4657i	0.182619	−	1.03568i	0.928976	−	0.370139i	$-0.120690\pi$
$654$	−1.24567	−	3.18042i	−0.0487097	−	0.124364i
$655$	−25.8231	+	21.6681i	−1.00899	+	0.846644i
$656$	−1.08865	−	1.88559i	−0.0425045	−	0.0736200i
$657$	40.3879	−	16.9589i	1.57568	−	0.661629i
$658$	−1.64967	+	2.85731i	−0.0643108	+	0.111390i
$659$	2.51054	+	14.2380i	0.0977969	+	0.554634i	0.993854	+	0.110696i	$0.0353078\pi$
$659$	2.51054	+	14.2380i	0.0977969	+	0.554634i	−0.896058	+	0.443938i	$0.853581\pi$
$660$	−0.664154	−	27.3950i	−0.0258522	−	1.06635i
$661$	−20.9378	+	7.62074i	−0.814387	+	0.296413i	−0.715435	−	0.698680i	$-0.753771\pi$
$661$	−20.9378	+	7.62074i	−0.814387	+	0.296413i	−0.0989522	+	0.995092i	$0.531549\pi$
$662$	16.5984	−	6.04133i	0.645116	−	0.234803i
$663$	7.84973	−	4.78939i	0.304858	−	0.186004i
$664$	−0.940067	−	5.33138i	−0.0364817	−	0.206898i
$665$	1.05467	−	1.82675i	0.0408985	−	0.0708382i
$666$	12.3252	+	19.1414i	0.477592	+	0.741715i
$667$	0.314326	+	0.544429i	0.0121708	+	0.0210804i
$668$	−10.4017	+	8.72804i	−0.402453	+	0.337698i
$669$	−17.0917	−	2.58830i	−0.660803	−	0.100069i
$670$	4.59316	−	26.0491i	0.177449	−	1.00636i
$671$	−11.9184	−	10.0007i	−0.460104	−	0.386073i
$672$	0.176612	−	0.524453i	0.00681296	−	0.0202312i
$673$	−23.4002	−	8.51699i	−0.902012	−	0.328306i	−0.150954	−	0.988541i	$-0.548234\pi$
$673$	−23.4002	−	8.51699i	−0.902012	−	0.328306i	−0.751059	+	0.660235i	$0.770457\pi$
$674$	−10.5429			−0.406096
$675$	−38.4342	+	9.70132i	−1.47933	+	0.373404i
$676$	8.89058			0.341945
$677$	−7.50239	−	2.73065i	−0.288340	−	0.104947i	0.193801	−	0.981041i	$-0.437918\pi$
$677$	−7.50239	−	2.73065i	−0.288340	−	0.104947i	−0.482141	+	0.876094i	$0.660141\pi$
$678$	−16.3489	+	3.29319i	−0.627877	+	0.126474i
$679$	−4.57053	−	3.83513i	−0.175401	−	0.147179i
$680$	0.700218	−	3.97113i	0.0268521	−	0.152286i
$681$	−22.8302	+	28.5875i	−0.874857	+	1.09547i
$682$	2.29079	−	1.92220i	0.0877187	−	0.0736048i
$683$	17.5306	+	30.3639i	0.670789	+	1.16184i	0.977681	+	0.210097i	$0.0673779\pi$
$683$	17.5306	+	30.3639i	0.670789	+	1.16184i	−0.306891	+	0.951745i	$0.599289\pi$
$684$	5.32348	+	1.65018i	0.203548	+	0.0630961i
$685$	−20.8057	+	36.0365i	−0.794944	+	1.37688i
$686$	0.771067	+	4.37294i	0.0294395	+	0.166960i
$687$	−35.3995	−	19.3094i	−1.35058	−	0.736701i
$688$	6.66967	−	2.42756i	0.254279	−	0.0925498i
$689$	3.54168	−	1.28907i	0.134927	−	0.0491095i
$690$	0.779254	+	0.425061i	0.0296657	+	0.0161818i
$691$	−0.344177	−	1.95193i	−0.0130931	−	0.0742548i	0.977561	−	0.210652i	$-0.0675587\pi$
$691$	−0.344177	−	1.95193i	−0.0130931	−	0.0742548i	−0.990654	+	0.136397i	$0.956448\pi$
$692$	−3.22220	+	5.58102i	−0.122490	+	0.212159i
$693$	3.13219	−	2.89816i	0.118982	−	0.110092i
$694$	−16.2523	−	28.1499i	−0.616930	−	1.06855i
$695$	−14.2927	+	11.9930i	−0.542152	+	0.454920i
$696$	−4.71171	+	5.89988i	−0.178597	+	0.223635i
$697$	0.429014	−	2.43306i	0.0162501	−	0.0921587i
$698$	−15.3747	−	12.9009i	−0.581942	−	0.488308i
$699$	45.3764	−	9.14025i	1.71629	−	0.345716i
$700$	2.29037	+	0.833627i	0.0865679	+	0.0315081i
$701$	42.8694			1.61916			0.809578	−	0.587013i	$-0.199696\pi$
$701$	42.8694			1.61916			0.809578	+	0.587013i	$0.199696\pi$
$702$	−20.1155	+	13.6532i	−0.759212	+	0.515308i
$703$	14.0984			0.531730
$704$	−4.18356	−	1.52269i	−0.157674	−	0.0573886i
$705$	20.2853	−	60.2376i	0.763990	−	2.26868i
$706$	8.45411	+	7.09384i	0.318174	+	0.266980i
$707$	0.134245	−	0.761342i	0.00504881	−	0.0286332i
$708$	−5.10820	−	0.773566i	−0.191978	−	0.0290724i
$709$	26.9016	−	22.5731i	1.01031	−	0.847752i	0.0219320	−	0.999759i	$-0.493018\pi$
$709$	26.9016	−	22.5731i	1.01031	−	0.847752i	0.988379	+	0.152008i	$0.0485738\pi$
$710$	14.3898	+	24.9239i	0.540041	+	0.935379i
$711$	−17.2736	+	33.5785i	−0.647812	+	1.25929i
$712$	−2.52624	+	4.37558i	−0.0946748	+	0.163982i
$713$	0.0168206	+	0.0953942i	0.000629935	+	0.00357254i
$714$	0.536041	−	0.327057i	0.0200608	−	0.0122398i
$715$	69.5590	−	25.3174i	2.60136	−	0.946818i
$716$	11.7577	−	4.27944i	0.439405	−	0.159930i
$717$	1.01000	+	41.6607i	0.0377193	+	1.55585i
$718$	−0.680852	−	3.86130i	−0.0254092	−	0.144103i
$719$	−7.52422	+	13.0323i	−0.280606	+	0.486024i	−0.971534	−	0.236899i	$-0.923869\pi$
$719$	−7.52422	+	13.0323i	−0.280606	+	0.486024i	0.690928	+	0.722924i	$0.257202\pi$
$720$	−1.34032	+	10.5765i	−0.0499509	+	0.394161i
$721$	0.318758	+	0.552105i	0.0118712	+	0.0205615i
$722$	−11.9109	+	9.99445i	−0.443279	+	0.371955i
$723$	−0.942147	−	2.40546i	−0.0350388	−	0.0894601i
$724$	0.0528764	−	0.299877i	0.00196513	−	0.0111448i
$725$	−25.4749	−	21.3760i	−0.946113	−	0.793883i
$726$	−10.1013	−	11.4622i	−0.374895	−	0.425403i
$727$	−13.7436	−	5.00226i	−0.509721	−	0.185523i	0.0743399	−	0.997233i	$-0.476315\pi$
$727$	−13.7436	−	5.00226i	−0.509721	−	0.185523i	−0.584061	+	0.811710i	$0.698537\pi$
$728$	1.49486			0.0554032
$729$	9.96884	−	25.0923i	0.369216	−	0.929343i
$730$	51.8884			1.92048
$731$	7.56813	+	2.75457i	0.279917	+	0.101882i
$732$	4.00196	+	4.54113i	0.147917	+	0.167845i
$733$	11.5481	+	9.69000i	0.426539	+	0.357908i	0.830644	−	0.556804i	$-0.187973\pi$
$733$	11.5481	+	9.69000i	0.426539	+	0.357908i	−0.404105	+	0.914713i	$0.632417\pi$
$734$	5.06206	−	28.7084i	0.186844	−	1.05964i
$735$	−15.4841	−	39.5336i	−0.571140	−	1.45822i
$736$	0.110473	−	0.0926974i	0.00407207	−	0.00341687i
$737$	−16.5689	−	28.6981i	−0.610322	−	1.05711i
$738$	−0.821199	+	6.48005i	−0.0302288	+	0.238534i
$739$	−23.9031	+	41.4014i	−0.879290	+	1.52297i	−0.0271676	+	0.999631i	$0.508649\pi$
$739$	−23.9031	+	41.4014i	−0.879290	+	1.52297i	−0.852122	+	0.523343i	$0.824685\pi$
$740$	4.68296	+	26.5584i	0.172149	+	0.976305i
$741$	0.364885	+	15.0508i	0.0134044	+	0.552904i
$742$	0.241854	−	0.0880275i	0.00887873	−	0.00323159i
$743$	43.7125	−	15.9101i	1.60366	−	0.583683i	0.623485	−	0.781835i	$-0.285716\pi$
$743$	43.7125	−	15.9101i	1.60366	−	0.583683i	0.980171	+	0.198152i	$0.0634940\pi$
$744$	−0.993143	+	0.605951i	−0.0364104	+	0.0222152i
$745$	−10.0538	−	57.0178i	−0.368342	−	2.08897i
$746$	−3.13591	+	5.43155i	−0.114814	+	0.198863i
$747$	−7.42933	+	14.4420i	−0.271825	+	0.528405i
$748$	−2.52589	−	4.37497i	−0.0923558	−	0.159965i
$749$	−2.17113	+	1.82179i	−0.0793312	+	0.0665668i
$750$	−15.9974	−	2.42258i	−0.584142	−	0.0884601i
$751$	0.306626	−	1.73897i	0.0111890	−	0.0634557i	−0.978702	−	0.205286i	$-0.934188\pi$
$751$	0.306626	−	1.73897i	0.0111890	−	0.0634557i	0.989891	+	0.141830i	$0.0452987\pi$
$752$	−7.91059	−	6.63778i	−0.288470	−	0.242055i
$753$	−8.05667	+	23.9244i	−0.293601	+	0.871854i
$754$	−19.1657	−	6.97575i	−0.697974	−	0.254042i
$755$	−55.5012			−2.01989
$756$	−1.37365	+	0.932350i	−0.0499590	+	0.0339093i
$757$	3.34143			0.121446			0.0607232	−	0.998155i	$-0.480659\pi$
$757$	3.34143			0.121446			0.0607232	+	0.998155i	$0.480659\pi$
$758$	25.3306	+	9.21957i	0.920048	+	0.334870i
$759$	1.09015	−	0.219590i	0.0395698	−	0.00797061i
$760$	5.05743	+	4.24369i	0.183452	+	0.153935i
$761$	8.29207	−	47.0267i	0.300587	−	1.70472i	−0.342994	−	0.939338i	$-0.611441\pi$
$761$	8.29207	−	47.0267i	0.300587	−	1.70472i	0.643581	−	0.765378i	$-0.277448\pi$
$762$	0.172083	−	0.215478i	0.00623390	−	0.00780594i
$763$	0.482660	−	0.404999i	0.0174735	−	0.0146620i
$764$	7.19635	+	12.4645i	0.260355	+	0.450948i
$765$	−8.87928	+	8.21585i	−0.321031	+	0.297045i
$766$	1.62814	−	2.82001i	0.0588269	−	0.101891i
$767$	−2.42343	−	13.7439i	−0.0875049	−	0.496265i
$768$	1.52055	+	0.829416i	0.0548681	+	0.0299290i
$769$	6.37595	−	2.32066i	0.229923	−	0.0836850i	−0.224490	−	0.974476i	$-0.572071\pi$
$769$	6.37595	−	2.32066i	0.229923	−	0.0836850i	0.454412	+	0.890791i	$0.349849\pi$
$770$	4.75004	−	1.72887i	0.171179	−	0.0623042i
$771$	−16.7635	−	9.14400i	−0.603722	−	0.329313i
$772$	0.529736	+	3.00428i	0.0190656	+	0.108126i
$773$	15.0683	−	26.0991i	0.541970	−	0.938720i	−0.456820	−	0.889559i	$-0.651012\pi$
$773$	15.0683	−	26.0991i	0.541970	−	0.938720i	0.998791	−	0.0491615i	$-0.0156549\pi$
$774$	−20.3384	−	6.30451i	−0.731049	−	0.226611i
$775$	−2.56205	−	4.43760i	−0.0920316	−	0.159403i
$776$	14.3052	−	12.0035i	0.513527	−	0.430900i
$777$	−2.62066	+	3.28153i	−0.0940158	+	0.117724i
$778$	0.241315	−	1.36857i	0.00865158	−	0.0490655i
$779$	3.09862	+	2.60005i	0.111020	+	0.0931565i
$780$	−28.2313	+	5.68668i	−1.01084	+	0.203616i
$781$	33.8808	+	12.3316i	1.21235	+	0.441260i
$782$	0.163638			0.00585169
$783$	21.9624	−	5.54362i	0.784873	−	0.198113i
$784$	−6.89792			−0.246354
$785$	−58.8782	−	21.4299i	−2.10145	−	0.764866i
$786$	5.24353	−	15.5708i	0.187031	−	0.555390i
$787$	12.3752	+	10.3840i	0.441127	+	0.370150i	0.836131	−	0.548530i	$-0.184812\pi$
$787$	12.3752	+	10.3840i	0.441127	+	0.370150i	−0.395004	+	0.918679i	$0.629257\pi$
$788$	3.86614	−	21.9260i	0.137725	−	0.781080i
$789$	22.5027	+	3.40772i	0.801117	+	0.121318i
$790$	−34.2653	+	28.7520i	−1.21911	+	1.02295i
$791$	−1.53818	−	2.66421i	−0.0546914	−	0.0947284i
$792$	7.23075	+	11.2296i	0.256933	+	0.399026i
$793$	−8.17525	+	14.1599i	−0.290312	+	0.502835i
$794$	0.371642	+	2.10769i	0.0131891	+	0.0747991i
$795$	−4.23268	+	2.58250i	−0.150118	+	0.0915918i
$796$	−23.0820	+	8.40117i	−0.818121	+	0.297772i
$797$	0.518033	−	0.188548i	0.0183497	−	0.00667873i	−0.332829	−	0.942987i	$-0.608003\pi$
$797$	0.518033	−	0.188548i	0.0183497	−	0.00667873i	0.351179	+	0.936308i	$0.385781\pi$
$798$	0.0249172	+	1.02779i	0.000882059	+	0.0363832i
$799$	−2.03474	−	11.5396i	−0.0719840	−	0.408242i
$800$	−3.81433	+	6.60661i	−0.134857	+	0.233579i
$801$	13.9754	−	5.86827i	0.493796	−	0.207345i
$802$	4.27666	+	7.40739i	0.151014	+	0.261564i
$803$	49.7973	−	41.7849i	1.75731	−	1.47456i
$804$	4.70167	+	12.0042i	0.165815	+	0.423354i
$805$	−0.0284329	+	0.161251i	−0.00100213	+	0.00568335i
$806$	−2.40742	−	2.02007i	−0.0847979	−	0.0711539i
$807$	11.8052	+	13.3956i	0.415561	+	0.471548i
$808$	2.27375	+	0.827576i	0.0799901	+	0.0291140i
$809$	−3.04561			−0.107078			−0.0535389	−	0.998566i	$-0.517050\pi$
$809$	−3.04561			−0.107078			−0.0535389	+	0.998566i	$0.517050\pi$
$810$	22.3953	−	22.8335i	0.786891	−	0.802289i
$811$	−7.71732			−0.270992			−0.135496	−	0.990778i	$-0.543263\pi$
$811$	−7.71732			−0.270992			−0.135496	+	0.990778i	$0.543263\pi$
$812$	−1.30878	−	0.476359i	−0.0459293	−	0.0167169i
$813$	−1.16182	−	1.31835i	−0.0407468	−	0.0462364i
$814$	25.8813	+	21.7170i	0.907138	+	0.761179i
$815$	−9.79944	+	55.5754i	−0.343259	+	1.94672i
$816$	0.716761	+	1.83001i	0.0250916	+	0.0640632i
$817$	−10.1011	+	8.47584i	−0.353393	+	0.296532i
$818$	−13.6359	−	23.6181i	−0.476769	−	0.825789i
$819$	−3.57104	−	2.71277i	−0.124782	−	0.0947919i
$820$	−3.86870	+	6.70079i	−0.135101	+	0.234002i
$821$	4.07282	+	23.0981i	0.142142	+	0.806129i	0.969617	+	0.244627i	$0.0786654\pi$
$821$	4.07282	+	23.0981i	0.142142	+	0.806129i	−0.827475	+	0.561502i	$0.810224\pi$
$822$	−0.491545	−	20.2752i	−0.0171446	−	0.707181i
$823$	28.0764	−	10.2190i	0.978683	−	0.356211i	0.197355	−	0.980332i	$-0.436765\pi$
$823$	28.0764	−	10.2190i	0.978683	−	0.356211i	0.781328	+	0.624121i	$0.214543\pi$
$824$	−1.87502	+	0.682450i	−0.0653193	+	0.0237743i
$825$	−50.2169	+	30.6391i	−1.74833	+	1.06672i
$826$	−0.165491	−	0.938544i	−0.00575816	−	0.0326561i
$827$	9.72093	−	16.8371i	0.338030	−	0.585485i	−0.646032	−	0.763310i	$-0.723573\pi$
$827$	9.72093	−	16.8371i	0.338030	−	0.585485i	0.984062	+	0.177825i	$0.0569062\pi$
$828$	−0.432127	+	0.0209649i	−0.0150174	+	0.000728581i
$829$	5.13594	+	8.89571i	0.178379	+	0.308961i	0.941325	−	0.337501i	$-0.109581\pi$
$829$	5.13594	+	8.89571i	0.178379	+	0.308961i	−0.762947	+	0.646461i	$0.776248\pi$
$830$	−14.7374	+	12.3661i	−0.511543	+	0.429235i
$831$	18.5495	+	2.80907i	0.643476	+	0.0974455i
$832$	−0.812454	+	4.60766i	−0.0281668	+	0.159742i
$833$	−5.99593	−	5.03118i	−0.207747	−	0.174320i
$834$	2.90222	−	8.61818i	0.100496	−	0.298423i
$835$	45.3433	+	16.5036i	1.56917	+	0.571132i
$836$	8.27099			0.286058
$837$	3.47214	+	0.354747i	0.120015	+	0.0122619i
$838$	16.0153			0.553241
$839$	12.6630	+	4.60894i	0.437174	+	0.159118i	0.551225	−	0.834357i	$-0.314161\pi$
$839$	12.6630	+	4.60894i	0.437174	+	0.159118i	−0.114051	+	0.993475i	$0.536383\pi$
$840$	−1.92786	+	0.388331i	−0.0665173	+	0.0133987i
$841$	−7.65820	−	6.42599i	−0.264076	−	0.221586i
$842$	−3.15120	+	17.8713i	−0.108597	+	0.615887i
$843$	−9.16212	+	11.4726i	−0.315560	+	0.395137i
$844$	−2.31292	+	1.94077i	−0.0796141	+	0.0668042i
$845$	−15.7971	−	27.3614i	−0.543438	−	0.941262i
$846$	6.85166	+	30.2125i	0.235565	+	1.03873i
$847$	1.40913	−	2.44068i	0.0484181	−	0.0838627i
$848$	0.139883	+	0.793316i	0.00480360	+	0.0272426i
$849$	9.58596	+	5.22887i	0.328989	+	0.179454i
$850$	−8.13426	+	2.96063i	−0.279003	+	0.101549i
$851$	−1.02839	+	0.374303i	−0.0352527	+	0.0128309i
$852$	−12.3142	−	6.71707i	−0.421879	−	0.230123i
$853$	8.25045	+	46.7906i	0.282490	+	1.60208i	0.714115	+	0.700028i	$0.246829\pi$
$853$	8.25045	+	46.7906i	0.282490	+	1.60208i	−0.431625	+	0.902053i	$0.642060\pi$
$854$	−0.558270	+	0.966953i	−0.0191036	+	0.0330884i
$855$	−4.38043	−	19.3155i	−0.149808	−	0.660577i
$856$	−4.43536	−	7.68227i	−0.151598	−	0.262575i
$857$	17.7848	−	14.9232i	0.607516	−	0.509766i	−0.286336	−	0.958129i	$-0.592437\pi$
$857$	17.7848	−	14.9232i	0.607516	−	0.509766i	0.893851	+	0.448363i	$0.147993\pi$
$858$	−22.5142	+	28.1918i	−0.768623	+	0.962451i
$859$	3.20736	−	18.1898i	0.109434	−	0.620629i	−0.879923	−	0.475117i	$-0.842406\pi$
$859$	3.20736	−	18.1898i	0.109434	−	0.620629i	0.989356	−	0.145513i	$-0.0464831\pi$
$860$	−19.3219	−	16.2130i	−0.658873	−	0.552860i
$861$	−1.18117	+	0.237925i	−0.0402542	+	0.00810847i
$862$	−2.00810	−	0.730889i	−0.0683962	−	0.0248942i
$863$	−21.1288			−0.719233			−0.359616	−	0.933100i	$-0.617092\pi$
$863$	−21.1288			−0.719233			−0.359616	+	0.933100i	$0.617092\pi$
$864$	−2.12724	−	4.74077i	−0.0723701	−	0.161284i
$865$	22.9014			0.778670
$866$	−23.6552	−	8.60978i	−0.803836	−	0.292572i
$867$	8.68544	−	25.7916i	0.294973	−	0.875928i
$868$	−0.164398	−	0.137946i	−0.00558003	−	0.00468220i
$869$	−9.73090	+	55.1867i	−0.330098	+	1.87208i
$870$	26.5293	+	4.01749i	0.899428	+	0.136206i
$871$	−26.6775	+	22.3851i	−0.903932	+	0.758489i
$872$	0.986018	+	1.70783i	0.0333908	+	0.0578345i
$873$	−55.9566	+	2.71477i	−1.89384	+	0.0918810i
$874$	−0.133958	+	0.232021i	−0.00453118	+	0.00784824i
$875$	−0.518268	−	2.93924i	−0.0175206	−	0.0993645i
$876$	−21.5891	+	13.1722i	−0.729427	+	0.445048i
$877$	−15.2356	+	5.54531i	−0.514471	+	0.187252i	−0.586191	−	0.810173i	$-0.699373\pi$
$877$	−15.2356	+	5.54531i	−0.514471	+	0.187252i	0.0717206	+	0.997425i	$0.477151\pi$
$878$	−24.2928	+	8.84187i	−0.819843	+	0.298399i
$879$	0.102137	+	4.21294i	0.00344498	+	0.142099i
$880$	2.74732	+	15.5808i	0.0926121	+	0.525230i
$881$	−22.2510	+	38.5398i	−0.749655	+	1.29844i	0.198333	+	0.980135i	$0.436447\pi$
$881$	−22.2510	+	38.5398i	−0.749655	+	1.29844i	−0.947988	+	0.318306i	$0.896886\pi$
$882$	16.4783	+	12.5179i	0.554853	+	0.421499i
$883$	−8.13325	−	14.0872i	−0.273706	−	0.474072i	0.696102	−	0.717943i	$-0.254916\pi$
$883$	−8.13325	−	14.0872i	−0.273706	−	0.474072i	−0.969808	+	0.243871i	$0.921583\pi$
$884$	−4.06693	+	3.41256i	−0.136786	+	0.114777i
$885$	6.69575	+	17.0954i	0.225075	+	0.574656i
$886$	2.42041	−	13.7268i	0.0813152	−	0.461162i
$887$	15.7565	+	13.2213i	0.529052	+	0.443928i	0.867774	−	0.496959i	$-0.165550\pi$
$887$	15.7565	+	13.2213i	0.529052	+	0.443928i	−0.338722	+	0.940887i	$0.609995\pi$
$888$	−8.69044	−	9.86126i	−0.291632	−	0.330922i
$889$	0.0478000	+	0.0173978i	0.00160316	+	0.000583502i
$890$	17.9549			0.601850
$891$	3.10530	−	39.9480i	0.104031	−	1.33831i
$892$	9.98040			0.334168
$893$	18.0276	+	6.56151i	0.603271	+	0.219573i
$894$	18.6574	+	21.1710i	0.623997	+	0.708065i
$895$	−34.0618	−	28.5813i	−1.13856	−	0.955367i
$896$	−0.0554807	+	0.314647i	−0.00185348	+	0.0105116i
$897$	−0.426205	−	1.08817i	−0.0142306	−	0.0363331i
$898$	22.3331	−	18.7397i	0.745266	−	0.625352i
$899$	1.46403	+	2.53578i	0.0488282	+	0.0845729i
$900$	21.1012	−	8.86040i	0.703373	−	0.295347i
$901$	−0.457035	+	0.791607i	−0.0152260	+	0.0263723i
$902$	1.68325	+	9.54617i	0.0560460	+	0.317853i
$903$	−0.0951963	−	3.92666i	−0.00316793	−	0.130671i
$904$	9.04797	−	3.29319i	0.300931	−	0.109530i
$905$	−1.01685	+	0.370102i	−0.0338011	+	0.0123026i
$906$	23.0922	−	14.0893i	0.767187	−	0.468087i
$907$	2.87345	+	16.2961i	0.0954113	+	0.541104i	0.994621	+	0.103585i	$0.0330315\pi$
$907$	2.87345	+	16.2961i	0.0954113	+	0.541104i	−0.899209	+	0.437519i	$0.855857\pi$
$908$	10.5612	−	18.2925i	0.350485	−	0.607058i
$909$	−3.92987	−	6.10322i	−0.130346	−	0.202431i
$910$	−2.65613	−	4.60055i	−0.0880498	−	0.152507i
$911$	20.5555	−	17.2481i	0.681033	−	0.571454i	−0.235275	−	0.971929i	$-0.575599\pi$
$911$	20.5555	−	17.2481i	0.681033	−	0.571454i	0.916308	+	0.400474i	$0.131155\pi$
$912$	−3.18152	−	0.481796i	−0.105351	−	0.0159539i
$913$	−4.18523	+	23.7356i	−0.138511	+	0.785534i
$914$	18.2304	+	15.2972i	0.603010	+	0.505985i
$915$	6.86482	−	20.3852i	0.226944	−	0.673914i
$916$	21.8767	+	7.96248i	0.722828	+	0.263088i
$917$	3.03073			0.100084
$918$	1.60873	−	5.67241i	0.0530959	−	0.187217i
$919$	−26.3725			−0.869947			−0.434974	−	0.900443i	$-0.643242\pi$
$919$	−26.3725			−0.869947			−0.434974	+	0.900443i	$0.643242\pi$
$920$	−0.481576	−	0.175279i	−0.0158771	−	0.00577879i
$921$	−40.2851	+	8.11469i	−1.32744	+	0.267388i
$922$	23.6044	+	19.8064i	0.777368	+	0.652289i
$923$	6.57970	−	37.3154i	0.216574	−	1.22825i
$924$	−1.53745	+	1.92515i	−0.0505783	+	0.0633329i
$925$	44.3479	−	37.2123i	1.45815	−	1.22353i
$926$	−18.0701	−	31.2983i	−0.593819	−	1.02852i
$927$	5.71765	+	1.77236i	0.187792	+	0.0582120i
$928$	2.17962	−	3.77521i	0.0715495	−	0.123927i
$929$	7.43411	+	42.1609i	0.243905	+	1.38326i	0.823021	+	0.568011i	$0.192287\pi$
$929$	7.43411	+	42.1609i	0.243905	+	1.38326i	−0.579116	+	0.815245i	$0.696602\pi$
$930$	3.62952	+	1.97980i	0.119017	+	0.0649202i
$931$	12.0421	−	4.38296i	0.394663	−	0.143646i
$932$	−25.1126	+	9.14025i	−0.822591	+	0.299399i
$933$	−16.4229	−	8.95820i	−0.537660	−	0.293278i
$934$	−6.42071	−	36.4137i	−0.210092	−	1.19149i
$935$	−8.97622	+	15.5473i	−0.293554	+	0.508450i
$936$	10.3025	−	9.53275i	0.336748	−	0.311588i
$937$	7.07409	+	12.2527i	0.231100	+	0.400278i	0.958132	−	0.286326i	$-0.0924341\pi$
$937$	7.07409	+	12.2527i	0.231100	+	0.400278i	−0.727032	+	0.686604i	$0.759101\pi$
$938$	−1.82175	+	1.52863i	−0.0594822	+	0.0499115i
$939$	−17.1761	+	21.5075i	−0.560520	+	0.701870i
$940$	−6.37241	+	36.1397i	−0.207845	+	1.17875i
$941$	19.8548	+	16.6602i	0.647249	+	0.543107i	0.906235	−	0.422775i	$-0.138944\pi$
$941$	19.8548	+	16.6602i	0.647249	+	0.543107i	−0.258986	+	0.965881i	$0.583388\pi$
$942$	29.9374	−	6.03034i	0.975413	−	0.196479i
$943$	−0.295055	−	0.107391i	−0.00960831	−	0.00349714i
$944$	2.98285			0.0970834
$945$	5.31013	+	2.57087i	0.172739	+	0.0836303i
$946$	−31.5994			−1.02738
$947$	−15.4336	−	5.61735i	−0.501523	−	0.182539i	0.0788559	−	0.996886i	$-0.474873\pi$
$947$	−15.4336	−	5.61735i	−0.501523	−	0.182539i	−0.580379	+	0.814347i	$0.697096\pi$
$948$	6.95778	−	20.6613i	0.225978	−	0.671046i
$949$	−52.3328	−	43.9125i	−1.69880	−	1.42546i
$950$	2.46102	−	13.9571i	0.0798461	−	0.452830i
$951$	5.54009	+	0.838970i	0.179650	+	0.0272055i
$952$	−0.277722	+	0.233036i	−0.00900102	+	0.00755275i
$953$	18.6267	+	32.2624i	0.603379	+	1.04508i	0.992305	+	0.123814i	$0.0395126\pi$
$953$	18.6267	+	32.2624i	0.603379	+	1.04508i	−0.388927	+	0.921269i	$0.627154\pi$
$954$	1.10549	−	2.14899i	0.0357917	−	0.0695760i
$955$	25.5736	−	44.2947i	0.827541	−	1.43334i
$956$	−4.17795	−	23.6943i	−0.135125	−	0.766330i
$957$	28.6954	−	17.5081i	0.927592	−	0.565955i
$958$	−36.0663	+	13.1271i	−1.16525	+	0.424116i
$959$	3.51553	−	1.27955i	0.113522	−	0.0413188i
$960$	−0.149179	−	6.15335i	−0.00481474	−	0.198598i
$961$	−5.30475	−	30.0847i	−0.171121	−	0.970475i
$962$	17.7529	−	30.7490i	0.572377	−	0.991386i
$963$	−3.34573	+	26.4010i	−0.107815	+	0.850761i
$964$	0.745760	+	1.29169i	0.0240193	+	0.0416027i
$965$	8.30465	−	6.96843i	0.267336	−	0.224322i
$966$	−0.0291046	−	0.0743091i	−0.000936426	−	0.00239086i
$967$	−1.72904	+	9.80587i	−0.0556022	+	0.315336i	−0.999906	−	0.0137404i	$-0.995626\pi$
$967$	−1.72904	+	9.80587i	−0.0556022	+	0.315336i	0.944303	+	0.329076i	$0.106737\pi$
$968$	6.75712	+	5.66990i	0.217182	+	0.182237i
$969$	−2.41408	−	2.73932i	−0.0775515	−	0.0879996i
$970$	−62.3598	−	22.6971i	−2.00225	−	0.728760i
$971$	2.62332			0.0841864			0.0420932	−	0.999114i	$-0.486597\pi$
$971$	2.62332			0.0841864			0.0420932	+	0.999114i	$0.486597\pi$
$972$	−3.52151	+	15.1855i	−0.112952	+	0.487075i
$973$	1.67746			0.0537771
$974$	−32.2397	−	11.7343i	−1.03303	−	0.375991i
$975$	40.8740	+	46.3807i	1.30901	+	1.48537i
$976$	−2.67705	−	2.24631i	−0.0856903	−	0.0719027i
$977$	−1.15268	+	6.53720i	−0.0368776	+	0.209143i	−0.997679	−	0.0680947i	$-0.978308\pi$
$977$	−1.15268	+	6.53720i	−0.0368776	+	0.209143i	0.960801	+	0.277238i	$0.0894191\pi$
$978$	−10.0310	−	25.6107i	−0.320755	−	0.818941i
$979$	17.2313	−	14.4588i	0.550716	−	0.462106i
$980$	12.2565	+	21.2289i	0.391520	+	0.678132i
$981$	0.743783	−	5.86917i	0.0237472	−	0.187388i
$982$	8.70382	−	15.0755i	0.277750	−	0.481077i
$983$	−8.23026	−	46.6761i	−0.262504	−	1.48874i	−0.776048	−	0.630673i	$-0.782779\pi$
$983$	−8.23026	−	46.6761i	−0.262504	−	1.48874i	0.513544	−	0.858063i	$-0.328332\pi$
$984$	−0.0914001	−	3.77008i	−0.00291373	−	0.120186i
$985$	−74.3484	+	27.0606i	−2.36894	+	0.862222i
$986$	4.64815	−	1.69179i	0.148027	−	0.0538775i
$987$	−4.87831	+	2.97642i	−0.155278	+	0.0947405i
$988$	−1.50937	−	8.56007i	−0.0480195	−	0.272332i
$989$	0.511786	−	0.886440i	0.0162739	−	0.0281871i
$990$	21.7120	−	42.2064i	0.690053	−	1.34141i
$991$	−22.0574	−	38.2046i	−0.700678	−	1.21361i	−0.968229	−	0.250066i	$-0.919548\pi$
$991$	−22.0574	−	38.2046i	−0.700678	−	1.21361i	0.267551	−	0.963544i	$-0.413786\pi$
$992$	0.514546	−	0.431755i	0.0163368	−	0.0137082i
$993$	30.2495	+	4.58086i	0.959938	+	0.145369i
$994$	0.449314	−	2.54819i	0.0142514	−	0.0808236i
$995$	66.8684	+	56.1092i	2.11987	+	1.77878i
$996$	2.99252	−	8.88633i	0.0948216	−	0.281574i
$997$	−46.8105	−	17.0376i	−1.48250	−	0.539587i	−0.531039	−	0.847348i	$-0.678198\pi$
$997$	−46.8105	−	17.0376i	−1.48250	−	0.539587i	−0.951464	+	0.307761i	$0.900420\pi$
$998$	26.2832			0.831981
$999$	2.86486	+	39.3282i	0.0906401	+	1.24429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.2.e.b.31.1	yes	12
3.2	odd	2		162.2.e.b.145.1		12
4.3	odd	2		432.2.u.b.193.2		12
9.2	odd	6		486.2.e.e.271.1		12
9.4	even	3		486.2.e.f.109.1		12
9.5	odd	6		486.2.e.g.109.2		12
9.7	even	3		486.2.e.h.271.2		12
27.2	odd	18		486.2.e.g.379.2		12
27.4	even	9		1458.2.c.f.973.1		12
27.5	odd	18		1458.2.c.g.487.6		12
27.7	even	9	inner	54.2.e.b.7.1	✓	12
27.11	odd	18		486.2.e.e.217.1		12
27.13	even	9		1458.2.a.g.1.6		6
27.14	odd	18		1458.2.a.f.1.1		6
27.16	even	9		486.2.e.h.217.2		12
27.20	odd	18		162.2.e.b.19.1		12
27.22	even	9		1458.2.c.f.487.1		12
27.23	odd	18		1458.2.c.g.973.6		12
27.25	even	9		486.2.e.f.379.1		12
108.7	odd	18		432.2.u.b.385.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.1	✓	12	27.7	even	9	inner
54.2.e.b.31.1	yes	12	1.1	even	1	trivial
162.2.e.b.19.1		12	27.20	odd	18
162.2.e.b.145.1		12	3.2	odd	2
432.2.u.b.193.2		12	4.3	odd	2
432.2.u.b.385.2		12	108.7	odd	18
486.2.e.e.217.1		12	27.11	odd	18
486.2.e.e.271.1		12	9.2	odd	6
486.2.e.f.109.1		12	9.4	even	3
486.2.e.f.379.1		12	27.25	even	9
486.2.e.g.109.2		12	9.5	odd	6
486.2.e.g.379.2		12	27.2	odd	18
486.2.e.h.217.2		12	27.16	even	9
486.2.e.h.271.2		12	9.7	even	3
1458.2.a.f.1.1		6	27.14	odd	18
1458.2.a.g.1.6		6	27.13	even	9
1458.2.c.f.487.1		12	27.22	even	9
1458.2.c.f.973.1		12	27.4	even	9
1458.2.c.g.487.6		12	27.5	odd	18
1458.2.c.g.973.6		12	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.14517 - 1.29945i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.617090 - 3.49969i) q^{5} +(0.631669 + 1.61276i) q^{6} +(-0.244752 + 0.205371i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.377165 + 2.97620i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.14517 - 1.29945i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.617090 - 3.49969i) q^{5} +(0.631669 + 1.61276i) q^{6} +(-0.244752 + 0.205371i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.377165 + 2.97620i) q^{9} +(-1.77684 + 3.07758i) q^{10} +(0.773091 + 4.38442i) q^{11} +(-0.0419788 - 1.73154i) q^{12} +(4.39657 - 1.60022i) q^{13} +(0.300233 - 0.109276i) q^{14} +(-5.25437 + 3.20587i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.567354 + 0.982686i) q^{17} +(1.37234 - 2.66771i) q^{18} +(-0.928896 - 1.60890i) q^{19} +(2.72228 - 2.28426i) q^{20} +(0.547153 + 0.0828588i) q^{21} +(0.773091 - 4.38442i) q^{22} +(0.110473 + 0.0926974i) q^{23} +(-0.552775 + 1.64147i) q^{24} +(-7.16859 - 2.60915i) q^{25} -4.67874 q^{26} +(4.29935 - 2.91815i) q^{27} -0.319501 q^{28} +(4.09634 + 1.49095i) q^{29} +(6.03396 - 1.21543i) q^{30} +(0.514546 + 0.431755i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.81203 - 6.02551i) q^{33} +(0.869237 - 0.729376i) q^{34} +(0.567702 + 0.983289i) q^{35} +(-2.20199 + 2.03746i) q^{36} +(-3.79438 + 6.57207i) q^{37} +(0.322602 + 1.82957i) q^{38} +(-7.11425 - 3.88062i) q^{39} +(-3.33937 + 1.21543i) q^{40} +(-2.04599 + 0.744678i) q^{41} +(-0.485817 - 0.264999i) q^{42} +(-1.23250 - 6.98988i) q^{43} +(-2.22603 + 3.85559i) q^{44} +(10.1830 + 3.15654i) q^{45} +(-0.0721058 - 0.124891i) q^{46} +(-7.91059 + 6.63778i) q^{47} +(1.08086 - 1.35342i) q^{48} +(-1.19781 + 6.79312i) q^{49} +(5.84389 + 4.90360i) q^{50} +(1.92667 - 0.388093i) q^{51} +(4.39657 + 1.60022i) q^{52} +0.805554 q^{53} +(-5.03813 + 1.27170i) q^{54} +15.8212 q^{55} +(0.300233 + 0.109276i) q^{56} +(-1.02694 + 3.04952i) q^{57} +(-3.33937 - 2.80206i) q^{58} +(0.517966 - 2.93753i) q^{59} +(-6.08577 - 0.921605i) q^{60} +(-2.67705 + 2.24631i) q^{61} +(-0.335846 - 0.581702i) q^{62} +(-0.518913 - 0.805889i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.88720 - 16.3741i) q^{65} +(-6.58267 + 4.01631i) q^{66} +(-6.99437 + 2.54574i) q^{67} +(-1.06628 + 0.388093i) q^{68} +(-0.00605383 - 0.249708i) q^{69} +(-0.197161 - 1.11816i) q^{70} +(4.04928 - 7.01356i) q^{71} +(2.76604 - 1.16146i) q^{72} +(-7.30065 - 12.6451i) q^{73} +(5.81333 - 4.87797i) q^{74} +(4.81879 + 12.3032i) q^{75} +(0.322602 - 1.82957i) q^{76} +(-1.08965 - 0.914324i) q^{77} +(5.35796 + 6.07981i) q^{78} +(11.8279 + 4.30501i) q^{79} +3.55368 q^{80} +(-8.71549 - 2.24503i) q^{81} +2.17729 q^{82} +(5.08715 + 1.85157i) q^{83} +(0.365883 + 0.415177i) q^{84} +(3.08899 + 2.59197i) q^{85} +(-1.23250 + 6.98988i) q^{86} +(-2.75360 - 7.03040i) q^{87} +(3.41047 - 2.86173i) q^{88} +(-2.52624 - 4.37558i) q^{89} +(-8.48932 - 6.44898i) q^{90} +(-0.747430 + 1.29459i) q^{91} +(0.0250421 + 0.142021i) q^{92} +(-0.0281968 - 1.16306i) q^{93} +(9.70378 - 3.53189i) q^{94} +(-6.20385 + 2.25802i) q^{95} +(-1.47857 + 0.902126i) q^{96} +(3.24273 + 18.3904i) q^{97} +(3.44896 - 5.97377i) q^{98} +(-13.3405 + 0.647222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more